David Deutsch's "The Beginning of Infinity" Ch 13 "Choices" Part 1, Ep 31

00:00:00.000 We want to be people of reason, or we should want to be people of reason,
00:00:04.480 both those things are actually the same. Indeed, we want our societies to be governed by reason.
00:00:10.720 The people, being people, have different preferences. How then should we go about deciding what
00:00:16.240 where's a society should do given differing viewpoints? Well, we vote, don't we? We enact
00:00:22.800 the will of the people. And to ensure we are reasonable when we go about doing this,
00:00:27.760 we should employ the tools of reason. Mathematics to the rescue, of course.
00:00:33.120 Indeed, there is a branch of mathematics called game theory. And within that,
00:00:38.000 an even narrower branch called social choice theory, which, as we will come to see,
00:00:43.520 animated such luminaries as von Neumann to try to set in mathematical stone the logical rules
00:00:50.160 for making decisions when people's preferences differed. The point of this chapter,
00:00:55.280 chapter 13 choices, as I see it anyway, is twofold. On the one hand, it is a defensive logic
00:01:01.520 and mathematics and reason more generally to solve problems, to solve real problems.
00:01:06.320 But on the other, it is a criticism of the idea that we can create pristine algorithms,
00:01:12.080 proofs, or whatever you like, of what we should do, how we should devote, what voting systems
00:01:18.320 we should implement, what decision algorithms we should try and legislate for,
00:01:23.360 so that we are always perfectly reasonable. The reason why that project has failed and will
00:01:30.000 always fail is because there exists in the mathematical universe and hence in the physical universe,
00:01:35.440 so-called no-go theorems. These no-go theorems can be used to show, or mathematically,
00:01:41.440 prove we might say, that there is no such thing, really, as the will of the people.
00:01:46.080 Now, as David writes on, and we'll come to this on page 338, there is no way to regard society
00:01:51.600 as a decision-maker with self-consistent preferences in the quote. Society is a thing that exists,
00:01:58.080 but it is not something analogous to a single mind which can indeed be said to have preferences,
00:02:03.760 but as we'll also come to say, things are even more complicated than that. It gets even worse,
00:02:08.480 because individual minds themselves must be inconsistent in some ways. So the whole purpose here,
00:02:14.800 and why this chapter has such an important role in the beginning of infinity,
00:02:19.680 is that we want to make choices that transform the world into a better place, don't we?
00:02:25.360 But any attempt to do this, by supposedly, perfectly rational means, will always meet with
00:02:30.640 paradoxes and irrationality. And this is because the conventional view of transforming the world
00:02:36.560 into a better place is to decide between the existing theories on offer. But in truth,
00:02:42.160 this is rarely actually the choice before us, whether it's in our own personal lives,
00:02:46.000 or as a society at large. We people create new explanations, which themselves transform the world.
00:02:52.960 And this misconception about what decision-making is, is what Sam Harris might call on his podcast,
00:02:58.560 one of the most pressing problems of our time, end quote. People get into terrible debates and
00:03:03.920 deadlock, and deadends in those debates over what should, and indeed must absolutely be done,
00:03:09.360 to solve some particular problem. But they fight over the existing solutions as though
00:03:15.200 they are the only possible solutions that shall ever present themselves, or then indeed,
00:03:20.240 this is how we should spend a great deal of our energy in debates over dead end solutions.
00:03:26.560 Rashing decision-making, as we will come to see on this worldview, and we're going to explore
00:03:33.040 this towards the more towards the end of the chapter, is more about choosing among explanations
00:03:39.760 and finding which is the best explanation once all the others have been successfully criticized.
00:03:46.560 And David makes his point here in this chapter and he's made it in many other places as well.
00:03:51.040 Having multiple explanations for any phenomena is exceedingly rare. One is lucky enough to be presented
00:03:57.440 with one single explanation, and in very rare cases we've got two. So rather often we have this
00:04:04.240 one explanation, and so it's called the explanation of whatever that thing happens to be.
00:04:08.160 And so that's the one that we use to direct rational human action, and where we lack a good
00:04:14.960 explanation, which is extremely often, then we have to create new explanations. We have to create
00:04:21.760 more knowledge, and this then helps us to increase the repertoire of choices that we have before
00:04:27.360 us. And this idea of having one good, namely one hard to vary, known, best explanation for a
00:04:35.680 given phenomena, applies to deciding among explanations itself. It's reflective. There is only
00:04:43.120 one known good explanation of how to decide among good explanations, and that's what we're going to
00:04:48.560 be discussing here in the chapter on choices. It extends into voting systems, which has an absolutely
00:04:53.600 crucial part of a functioning society. There really are worse voting systems, and where they
00:04:59.280 exist, they tend towards irrational outcomes more than the alternative, best system would. So this
00:05:05.360 chapter begins with an extended and pretty detailed investigation into, and it's seemingly quirky,
00:05:11.760 but as well, it's being used as an example of the irrationality that can creep into apparently
00:05:18.000 perfectly rational systems. But it begins with the example of the United States House of
00:05:24.240 Representatives of all things, and it talks about how the seats are allocated there in the
00:05:30.080 United States House of Representatives. Now, although very interesting in itself, it seems rather
00:05:34.320 parochial, which is unusual for the beginning of infinity. But really, this discussion about
00:05:40.560 the United States House of Representatives is just serving as a case study about how to
00:05:44.880 rationally make decisions. In this case, how can it be rationally decided to allocate the correct
00:05:52.000 number of seats per state to the House of Rips? Now, at times in this chapter, I'm going to
00:05:57.040 skim, because there is a lot of detail here. So I'll skim part of the chapter, which isn't
00:06:01.760 typically my practice, normally I'll read a chunk and then tell you when I'm leaving out a bit,
00:06:06.720 but I might not do this this time just to make things flow a little better. So I might be leaving
00:06:12.080 out lots, but I won't be telling you that I'm leaving out lots. So I'd urge you if you need more,
00:06:17.280 indeed, you must go to chapter 13 choices, because I'll be leaving out some and at times I won't
00:06:24.400 be making you aware of it. And the reason the chapter is so detailed is because David really does do
00:06:29.920 a comprehensive overview of just about all the objections that the reader might reasonably raise
00:06:35.040 as he presents each problem with the voting system. And this is because in a rather astonishing way,
00:06:41.360 each simple logical or mathematical solution to the problem being raised itself creates new
00:06:49.040 problems. So each time that this is of course common in science and mathematics in general,
00:06:53.200 but here it is especially illuminating that you think, oh, why don't they just and David will talk
00:06:58.720 about this? Why don't they just ID that there might be a very simple solution, clear or obvious
00:07:06.080 to most people thinking about the topic, but when pursued through to its logical conclusion itself
00:07:11.840 causes logical problems. And so just for illustrative purposes, I'll only talk about a couple of
00:07:19.120 these problems myself. And so you need to go to the book because the the upshot of it all is
00:07:24.800 even when the full force of mathematics and the best mathematicians indeed are applied to
00:07:30.320 seemingly trivial problems like how do we fairly allocate the number of seats in the house of
00:07:35.280 reps among the states insoluble problems and paradoxes arise. And that should be a concern to
00:07:41.280 anyone who thinks they can like Dr. Spock or some other Vulcan from Star Trek be perfectly logical
00:07:47.040 all or almost all of the time. So what's the parable of all this going to be? Well,
00:07:52.640 creativity is needed. So this chapter is very much a beginning of infinity. And although David does
00:07:59.600 not really mention the term in this chapter, he doesn't he doesn't highlight it that much,
00:08:04.400 it's always there beneath the surface that it's very much about morality. It's an investigation
00:08:10.960 into the logic of morality. Now, after all, morality is very much the question of what to do next,
00:08:17.760 how to choose among the options presented to you about what to do next, or how to possibly
00:08:24.160 in more, more often the cases given that the choices before you are unsatisfactory,
00:08:30.400 one must deploy their creativity in order to create a new and better choice than the ones that
00:08:38.480 exist. And this idea that morality is about what to do next, more on that in David's second
00:08:46.320 interview with Sam Harris on the Making Sense podcast, morality is about choices deciding what to do.
00:08:52.800 So let's begin the chapter and let's look at the logic of decision making and how we can make
00:08:58.800 better choices both personally and as a society.
00:09:18.080 So hello, welcome to topcast after that lengthy introduction. Chapter 13 choices, diving straight
00:09:25.920 in. In March 1792, George Washington exercised the first presidential veto in the history of the
00:09:32.720 United States of America. Unless you already know what he and Congress were quarreling about,
00:09:38.000 I doubt you will be able to guess, yet the issue remains controversial to this day.
00:09:43.120 With hindsight, one may even perceive a certain inevitability in it. For, as I shall explain,
00:09:48.400 it is rooted in a far-reaching misconception about the nature of human choice, which is still prevalent.
00:09:54.400 Paul said my reflection, what an introduction to the chapter. I mean, far-reaching misconception
00:10:01.200 about the nature of human choice. So this is why we're looking at this rather parochial, quirky
00:10:08.640 little example. And as I said in my introduction, I'm just going to skim read through parts of this
00:10:15.760 back to the book on the face of it. The issues seems no more than a technicality. In the US House
00:10:21.040 of Representatives, how many seats should each state be allotted? This is known as the
00:10:27.840 apportionment problem, because the US Constitution requires seats to be apportioned among the
00:10:34.720 several states, according to their respective numbers, or either respective populations.
00:10:40.000 So if your state contained 1% of the US population, it would be entitled to 1% of the seats in
00:10:45.120 the House. This was intended to implement the principle of representative government, that the
00:10:50.400 legislature should represent the people. It was, after all, about the House of Representatives,
00:10:56.160 the US Senate in contrast, represents the states of the Union, and hence each state, regardless
00:11:02.000 of population, has two senators. Just as a parochial aside, very similar to the Australian Senate,
00:11:08.640 except we have far fewer states, and so we have more senators per state. We've got 12 senators
00:11:17.360 from each state here in Australia, for anyone's interest, and that quirky piece of trivia.
00:11:22.080 Back to the book. At present, there are 435 seats in the House of Representatives. So if 1% of the US
00:11:28.560 population did live in your state, then by strict proportionality, the number of representatives
00:11:33.920 to which it would be entitled, known as its quota, would be 4.35. When the quotas are not
00:11:40.560 whole numbers, which of course they hardly ever are, they have to be rounded somehow. The method
00:11:45.440 of rounding is known as the apportionment rule. The Constitution did not specify an apportionment
00:11:50.480 rule. It left such details to Congress, and that is where the centuries of controversy began,
00:11:56.080 pause their moral affliction. The bulk of this first half of the chapter, I suppose, is all about
00:12:04.240 this. So you've got this idea that the House of Representatives has to be representative of the people,
00:12:12.400 and so if the state has 1% of the population, then it should be entitled to 1% of the seats in
00:12:17.600 the House of Representatives. But because the number of seats in the House of Representatives is
00:12:21.840 clearly always going to be far, far smaller than the number of people in the entire United States,
00:12:26.880 there's going to be this rounding problem. So you might very well round down or you might very
00:12:31.280 well round up. Whether you choose to round in one particular way or another is going to be called
00:12:37.120 the apportionment rule. So this is going to be the source of lots and lots of really interesting
00:12:45.680 paradoxes and problems. I'm going to come to the point that there can be no such perfectly
00:12:50.400 rational fair apportionment rule, but that's kind of stealing the thunder from later on.
00:12:57.040 But let's go back to the book. An apportionment rule is said to stay within the quota of the number
00:13:02.400 of seats that it allocates to each state, never differs from the state's quota by as much as the
00:13:06.880 whole seat. For instance, if a state's quota is 4.35 seats, then to stay within the quota,
00:13:13.440 a rule must assign that state either four seats or five. It may take all sorts of information into
00:13:19.120 account and choosing between four and five, but if it is capable of assigning any other number,
00:13:23.920 it is said to violate quota. Right. That seems perfectly fair and reasonable. Let's keep going.
00:13:31.200 When one first hears of the apportionment problem, compromises that seem to solve it at a stroke
00:13:36.400 spring easily in mind. Everyone asks, why couldn't they just, here is what I asked,
00:13:43.120 why couldn't they just round each state's quota to the nearest whole number? Under that rule,
00:13:47.600 a quota of 4.35 seats would be rounded down to four, 4.6 seats would be rounded up to five.
00:13:53.040 It seemed to me that since this sort of rounding can never add or subtract more than half a seat,
00:13:58.080 it would keep each state within half a seat of its quota, thus staying within the quota,
00:14:02.320 with room to spare. I was wrong. My rule violates quota. This is easy to demonstrate by applying
00:14:08.800 it to an imaginary house of representatives with ten seats in a nation of four states.
00:14:14.160 Suppose that one of the states has just under 85% of the total population and that the other
00:14:19.680 three of just over 5% each. The large state therefore has a quota of just under 8.5, which my rule
00:14:27.040 rounds down to eight. Each of the three small states has a quota of just over half a seat,
00:14:31.600 which my rule rounds up to one, but now we have allocated 11 seats, not 10.
00:14:38.320 In itself that hardly matters, the nation merely has one more legislated feed and planned.
00:14:42.640 The real problem is that this apportionment is no longer representative. 85% of 11 is not 8.5,
00:14:50.960 but 9.35. So the large state with only 8 seats is in fact short of its quota by well over one seat.
00:14:58.560 My rule under represents 85% of the population. Because we intended to allocate 10 seats,
00:15:05.200 the exact quotas necessarily add up to 10, but the rounded ones add up to 11.
00:15:10.800 And if there are going to be 11 seats in the house, the principle of representative
00:15:14.400 government and the constitution requires each state to receive its fair share of those,
00:15:19.200 not of the 10 we merely intended, paused the MRI reflection. And so that's where we begin.
00:15:25.280 That's where the problems come. Rounding, it seems simple, it seems logical, it seems fair,
00:15:31.840 and it's not. It can't be logical and fair all at once. And this is what we're going to have
00:15:36.880 example after example here in the book about. So going back to the book. Again, many why don't
00:15:43.040 they just ideas spring to mind. Why don't they just create three additional seats and give
00:15:46.480 them to the large state thus bringing the allocation within quota? Why don't they just transfer a
00:15:50.400 seat from one of the small states to a large state? Perhaps it should be from the state with
00:15:54.080 the smallest population. So it's the disadvantage as few people as possible. That would not only
00:15:58.240 bring all the allocations within the quota, but also restore the number of seats to the
00:16:01.520 originally intended 10. Such strategies are known as reallocation schemes. They are indeed capable
00:16:07.920 of staying within the quota. So what's wrong with them? In the jargon of the subject, the answer
00:16:12.880 is apportionment paradoxes or an ordinary language unfairness and irrationality. For example,
00:16:18.000 the last reallocation scheme that I described, which was where we just take the seat from the
00:16:22.880 smallest state and we give it to the largest state so that we have things back within quota.
00:16:26.960 That last reallocation scheme that I described is unfair by being biased against the inhabitants
00:16:32.720 of the least popular state. They bear the whole cost of correcting the rounding errors. On this
00:16:37.040 occasion, their representation has been rounded down to zero. Yet in the sense of minimizing the
00:16:41.760 deviation from the quotas, the apportionment is almost perfectly fair. Previously, 85% of the population
00:16:46.800 were well outside quota and now all are within it and 95% of the population are at the closest
00:16:53.440 whole numbers to their quotas. It is true that now 5% have no representatives so they will not be
00:16:58.960 able to vote in congressional elections at all. But that still leaves them within the quota and
00:17:03.840 indeed only slightly further from their exact quota that they were. Nevertheless, because those
00:17:09.040 5% have been completely disenfranchised, most advocates of representative government would regard
00:17:15.440 this outcome as much less representative than what it was before. Okay, now I'm skipping a
00:17:21.520 vast amount right now. I've just skimmed a little bit there, but I'm just taking out a whole
00:17:26.560 bunch here. David goes through a bunch of other problems of the sort, why don't they just?
00:17:33.120 The upshot of all this is that none of them are able to fairly apportion the seats without
00:17:39.520 some of the problems arising. David gets to the point where he talks about all these other
00:17:45.760 apportionment rules and over the years, and he writes, Congress has continually debated and tinkered
00:17:51.520 with the rules of apportionment. Jefferson came up with a rule and it was put in place, but it was
00:17:56.800 dropped in 1841 in favour of one proposed by another senator, Daniel Webster, which does use
00:18:03.280 reallocation. Now that one also violates quota, but very rarely, and it was, like Hamilton's rule,
00:18:08.800 deemed to be impartial between states. A decade later, Webster's rule was in turn dropped in
00:18:14.880 favour of Hamilton's. The latter's supporters now believed that the principle of representative
00:18:19.120 government was fully implemented, and perhaps hope that this would be the end of the apportion
00:18:22.720 problem, but they were disappointed. It was soon causing more controversy than ever, because
00:18:28.000 Hamilton's rule, despite its impartiality and proportionality, began to make allocations that
00:18:33.600 seemed outrageously perverse. Paul's M.R. Reflection, so we, after some discussion, we've come to
00:18:40.080 the understanding that there was this rule. Hamilton's rule, Hamilton came up with this rule,
00:18:44.160 which seemed to be impartial and proportional. However, it started to make allocations that
00:18:50.240 seemed outrageously perverse. So going back to the book. For instance, it was susceptible to what
00:18:56.320 came to be called the population paradox. A state whose population has increased since the last
00:19:02.160 census can lose a seed. To one whose population has decreased. Say that again, a state whose
00:19:08.960 population has increased since the last census can lose a seed to one whose population has
00:19:14.320 decreased. So that seems absurd, doesn't it? So that's the population paradox. We're going to come
00:19:19.920 back to the population paradox again and again. So just keep that in mind. This idea, the population
00:19:24.480 paradox is if your state's population increase, as you might very well lose a seed to someone
00:19:29.520 who, some other state, where their population has decreased, which is weird. And then David goes
00:19:34.880 through solutions suggested to the population paradox and all the wider than they just
00:19:43.120 attempts to solve that. And David talks about the various rules. So there was a rule that
00:19:48.800 rule that tried to avoid these population paradoxes and things. Hamilton's rule was one,
00:19:55.280 Webster's rule was another. And David writes, after Hamilton's rule was adopted, in 1851,
00:20:01.200 Webster still enjoyed substantial support. So Congress tried on at least two occasions,
00:20:06.400 a trick that seemed to provide a judicious compromise. Adjust the number of seats in the house
00:20:11.760 until the two rules agree. Surely that would please everyone. Yet the upshot of that was,
00:20:18.080 in 1871, some states considered the result to be so unfair and the ensuing compromise legislation
00:20:24.480 was so chaotic that it was unclear what allocation rule, if any, had been decided upon.
00:20:30.320 The apportionment that was implemented, which included last minute,
00:20:33.920 which included the last minute creation of several additional seats for now apparent reason,
00:20:38.080 satisfied neither Hamilton's rule nor Webster's, many considered it unconstitutional.
00:20:44.080 For the next few decades, after 1871, every census saw either the adoption of a new
00:20:48.720 apportionment rule or change in the number of seats designed to compromise between different rules.
00:20:54.080 In 1921, no apportionment was made at all. They kept the old one, a course of action that may
00:20:58.560 well have been unconstitutional again because Congress could not agree on a rule.
00:21:03.360 The apportionment issue has been referred several times to eminent mathematicians,
00:21:08.400 including twice to the National Academy of Sciences and on each occasion,
00:21:13.280 these authorities have made different recommendations. Yet none of them ever accused
00:21:18.000 of predecessors of making errors in mathematics. This ought to have warned everyone that this
00:21:23.520 problem is not really about mathematics, and on each occasion when the experts' recommendations
00:21:28.800 were implemented, paradoxes and disputes kept on happening. In 1901, the Census Bureau
00:21:35.200 published a table showing what the apportionments would be for every number of seats between
00:21:40.240 350 and 400 using Hamilton's rule. By quirk of arithmetic of a kind that is common in
00:21:46.480 apportionment, Colorado would get three seats for each of these numbers except for 357,
00:21:53.280 when it would get only two. The chairman of the House Committee on Apportionment,
00:21:56.960 who was from Illinois, I do not know whether or not anything against Colorado,
00:22:00.480 proposed that number of seats be changed to 357, and that Hamilton's rule will be used.
00:22:05.600 This proposal was regarded with suspicion and Congress eventually rejected it,
00:22:09.920 adopting a 386 member apportionment and Webster's rule, which also gave Colorado its
00:22:14.880 rightful three seats. But was that apportionment really any more rightful than Hamilton's
00:22:20.000 rule with 357 seats? By what criterion? Majority voting among apportionment rules? What exactly
00:22:26.400 would be wrong with working out what a large number of rival apportionment rules would do,
00:22:30.960 and then allocating to each state the number of representatives but the majority of the schemes
00:22:35.120 would allocate? The main thing is that that itself is an apportionment rule. Similarly,
00:22:40.960 combining Hamilton's and Webster's schemes as they tried to do in 1871 just constituted
00:22:45.440 adopting a third scheme. And what does such a scheme have going for it? Each of its constituent
00:22:51.200 schemes was presumably designed to have some desirable properties. A combined scheme that was
00:22:56.160 not designed to have those properties will not have them except by coincidence. So it will not
00:23:00.720 necessarily inherit the good features of its constituents. It will inherit some good ones and some
00:23:05.440 bad ones and have additional good and bad features of its own. But if it was not designed to be
00:23:09.680 good, why should it be? Pause their my reflection. And here I'm going to utterly and completely
00:23:16.720 steal David's thunder from towards the end of the chapter. Because it's one of the most profound
00:23:23.440 things that I read in the book and so, and it has really changed my thinking on this particular
00:23:28.480 matter. David will come to it, but I just want to flag it now because he's talked there about
00:23:33.280 why not, if you've got these two schemes that are designed to try and solve the problem of
00:23:40.240 apportionment, why not pick one that's sort of halfway in between these two? As we'll come to see,
00:23:47.120 this is the idea of compromise out there in the world. Compromise is a thing that is lauded as a
00:23:54.160 virtue in politics. But if you have two sides of the debate and over here on side A, they come up
00:24:03.040 with a particular solution, their purported solution called that solution X. And over here on side B,
00:24:09.840 they have a different solution altogether, a purported solution or policy and call that theory Y.
00:24:16.080 Now, if they're at loggerheads and they can't agree, it's supposedly a virtue to come to some
00:24:21.760 compromise. Compromise has, as David will say later on, an unfairly high reputation. In fact,
00:24:31.360 compromises are not good. The reason why compromise is not good is because a compromise is a third
00:24:37.680 option. And if you have two groups of people debating among themselves, it could be two political
00:24:43.280 parties, it could just be two people. And A wants to do this thing and B wants to do that thing.
00:24:49.360 The reason A wants to do this thing is because they've got an explanation in their mind,
00:24:52.560 they've got a theory in their mind about why this particular thing thing X is the best thing to do.
00:24:57.360 And this group of people over here or this person B here thinks that no X is wrong,
00:25:03.760 Y is the best thing to do. And I have a good explanation in my head as to why Y is the correct
00:25:09.200 thing to do. Now, if in fact you believe in compromise, then you will say, well, you can't
00:25:14.720 decide among you. Therefore, what you should do is you should do this third thing, this thing Z.
00:25:19.840 Why shouldn't we do that? At least we're doing something. The problem is that if you do Z,
00:25:25.200 if A and B, if they're groups of people, they could be the whole population, they could just be
00:25:29.920 two people in the partnership. If they decide to do this third thing Z, and if this third thing Z or
00:25:36.960 Z if you're American, if they do that thing, and then that thing fails, which invariably it does,
00:25:44.160 certainly in politics, so many political policies and theories fail when Z fails, when the third
00:25:52.320 option fails, no one learns anything. Neither group A nor group B actually ever endorsed Z.
00:26:01.840 They didn't think that Z was the best idea. They didn't think Z was a particularly good
00:26:05.920 idea at all. They thought that either X or Y was the best idea. So when Z fails, what happens?
00:26:13.040 Both A goes back to endorsing X again, and B goes back to endorsing Y again. They both revert to
00:26:21.120 their original positions. And so then what do you do? You just do another compromise? Why should
00:26:25.760 the compromise be better given that both X and Y think they've got a good explanation about why
00:26:31.040 their particular theory is the best theory? Wouldn't it be a better, more parsimonious idea to
00:26:35.920 actually try out X? If we try out X and X is shown to fail, great. Everyone has actually learned
00:26:43.680 something. A can no longer be committed to X is actually being the thing that will work and solve
00:26:48.800 the problem, because they've learned that it fails. So then everyone can get behind the alternative
00:26:53.360 now. Everyone can do their best to implement Y. Now Y might very well fail as well, but at least
00:27:02.160 we're learning things. We're making progress. We're ruling out stuff. We're not ruling out random
00:27:06.240 things that no one thought was a good idea in the first place. If you're going to do the compromise,
00:27:10.960 you may as well just be flipping your coin about what to do next, because no one really has a good
00:27:15.040 idea. Now it might very well be the case, of course, that X or Y could succeed. We might expect at
00:27:22.560 least one of them to succeed, because a whole bunch of creative people have good explanations in
00:27:27.520 their mind anyway. They have explanations as to why either X or Y should succeed, but neither of the
00:27:32.400 groups. No one has a good explanation as to why Z should actually work. And so when Z fails, that's
00:27:39.280 why we say no one learns anything. No one's explanation has been refuted. Indeed, there was no
00:27:44.720 explanation why Z should work at all in the first place. Z has perhaps some of the good features of
00:27:50.640 X and some of the good features of Y, but it will also have the bad features of X and the bad
00:27:55.120 features of Y. And perhaps more of the bad features of both than either on their own. And it will
00:28:00.400 have some good features of its own and some terrible features of its own. But we shouldn't expect
00:28:05.680 it to work, because no one has an explanation about why it should work, compared to X and Y,
00:28:11.200 where two groups of people or two individuals do have an explanation in their minds by their
00:28:17.360 lights as to why this thing should work. And that's why it should be tried. And that's why
00:28:21.600 compromise is bad, especially in politics, and yet compromises held up as this virtue of the
00:28:27.280 way in which politics should proceed, because people say at least the government is therefore
00:28:31.760 doing something. Many of us of course think that when the government does nothing, that's great,
00:28:37.680 and the processes that are in place in governments are there for a particular reason to actually
00:28:43.600 cause gridlocked, to actually cause things to stop, so that we can't have these terrible
00:28:50.480 compromises. So the institutions are there to slow things down, but many people believe in this
00:28:56.480 idea of just ramming through any old thing, so that something at least is getting done. Government
00:29:02.720 should do something. Many of us think government shouldn't do much at all. Government should be
00:29:08.720 restrained from doing too much, because it tends to do damage when it does anything at all.
00:29:14.800 Not always the case, there are legitimate reasons for government, at least some of this think that.
00:29:21.040 But we like to constrain the ability of government to do stuff, because more often than not,
00:29:28.000 it's coming up with compromises that no one believes in, or it's coming up with bad ideas,
00:29:32.560 and it's causing damage rather than finding solutions to our most pressing problems.
00:29:38.080 Okay, after that rant, let me go back to the book. David writes,
00:29:43.680 A devil's advocate might now ask, if majority voting among apportionment rules is such a bad
00:29:48.240 idea, why is majority voting among voters a good idea? It will be disastrous to use it and say
00:29:53.680 science. There are more astrologers than astronomers, and believers in paranormal phenomenon often
00:29:59.280 point out that purported witnesses of such phenomena outnumber the witnesses of most scientific
00:30:04.320 experiments by a large factor. So they demand proportionate credence, yet science refuses to judge
00:30:10.080 evidence in that way. It sticks with the criterion of good explanation. So if it would be wrong
00:30:14.720 for science to adopt that democratic principle, why is it right for politics, pause their
00:30:18.880 my reflection? Yes, so for my listeners and viewers that might be new to some of these ideas,
00:30:27.200 there is in the public mind, it would seem, an idea of scientific consensus.
00:30:32.080 Now to some extent, this has validity. Now there is a sense in which scientific, the consensus
00:30:46.480 of the scientists has some validity, and it's when a layperson is trying to decide what is
00:30:53.760 scientific knowledge in any particular time. So given a particular area that is not your
00:31:00.080 area of expertise, a good rule of thumb is to presume that whatever the scientific consensus is
00:31:07.360 among the experts in that area is the best theory or the best explanation at a given time.
00:31:13.920 That doesn't mean that it's true, it just means that that's the best explanation we have,
00:31:18.160 and we should take seriously the best explanations that we have at any particular time.
00:31:22.320 But scientific consensus is not the way we adjudicate between theories, not in science. Clearly,
00:31:30.160 every single good scientific theory was once a minority view, was once understood only by a
00:31:37.600 single mind or a small team of people, more than likely only a single mind in any particular time.
00:31:43.120 So once upon a time, the theory of general relativity was only understood by Albert Einstein,
00:31:50.960 and no one else. So he had an exceedingly minority view, but we don't take a vote among scientists
00:31:57.680 to decide what is true in physics. We let the theories compete one against the other,
00:32:04.640 and the competition is in light of a crucial experiment. That's in fact the way in which we
00:32:10.240 decide between theories of gravity let's say, which is what happened back in 1919 with Eddington's
00:32:15.600 experiment, which decided between Albert Einstein's general theory of relativity and Newton's
00:32:23.280 universal law of gravitation. Now that's a trope example, but the same is true of any other
00:32:30.000 area of science, where there are competing theories, competing explanations as to what accounts
00:32:36.640 for the phenomena in question. But it is not a vote among scientists that decides things.
00:32:43.600 It is experiment that decides. It is observation that decides between theories. It is the
00:32:48.480 evidence that decides between theories. But people who perhaps don't understand at the science,
00:32:54.560 let's say astrologers, there's more astrologers than astronomers. There's more people that
00:32:59.760 believe they have an understanding of astrology than would say they have an understanding of
00:33:03.680 astronomy or even an interesting one compared to the other. But we don't therefore conclude on that
00:33:08.880 basis that the majority should hold sway, that therefore astrologers should be funded by government
00:33:16.960 institutions, let's say. We do fund astronomers, not because there's more of one than the other,
00:33:22.640 but because there is there are objective ways of measuring or comparing the theories of one
00:33:31.040 subject against reality that aren't available in the other other. There is, I guess there are
00:33:36.880 certain ways of measuring astrology against reality, but they typically come up bad for astrology.
00:33:43.840 Whatever the case, if we can appreciate the fact that democratic voting is not the rational means
00:33:52.960 by which we come to gain truth or gain better explanations in the area of science,
00:33:59.040 why should democratic vote be the best way of deciding what is best, what is the truer moral choice
00:34:10.240 to make in the sphere of politics? Why does democratic vote good in one area and not in the other?
00:34:16.240 Let me just reread what David said here. So if it would be wrong for science to adopt that
00:34:22.720 democratic principle, why is it right for politics? Is it just because, as Churchill put it, many forms
00:34:30.240 of government have been tried and will be tried in this world of sin and war? No one
00:34:35.360 pretends that democracy is perfect or all wise, indeed it has been said, that democracy is the
00:34:41.040 worst form of government except for all those others that have been tried from time to time.
00:34:46.800 That would indeed be a sufficient reason, but there are cogent positive reasons as well,
00:34:51.760 and they tour about explanation as I shall explain. Some politicians have been so perplexed
00:34:57.280 by the sheer perverseness of apportionment paradoxes that they have been reduced to denouncing mathematics
00:35:02.480 itself. Representative Roger Q. Mills of Texas complained in 1882. I'm not going to try a Texan
00:35:08.640 accent here, that's for sure. I thought that mathematics was a divine science. I thought that
00:35:12.880 mathematics was the only science that spoke to inspiration and was infallible in its utterances,
00:35:17.520 but here is a new system of mathematics that demonstrates the truth to be false. In 1901,
00:35:23.840 Representative John E. Littlefield, whose own seat in Maine was under threat from the Alabama
00:35:28.320 paradox, said, God helped the state of Maine when mathematics reached for her and undertake to
00:35:33.280 strike her down. As a matter of fact, there is no such thing as mathematical inspiration,
00:35:38.400 mathematical knowledge coming from an infallible source, traditionally God.
00:35:42.000 As I've explained in chapter 8, our knowledge of mathematics is not infallible. This is the
00:35:49.040 mathematicians' misconception to a large extent. David has written very eloquently and spoken
00:35:56.320 very eloquently about this idea in various places. I just want to emphasize it again,
00:36:01.680 it's been said many times in this series. But the point is, mathematics is not infallible.
00:36:09.520 Mathematics does not give you certain truth. Mathematics does not even give you necessary truth.
00:36:16.400 But that's sinking for a moment. That angers certain mathematicians. They think that mathematics
00:36:23.280 is a privileged kind of knowledge. I know that I have encountered certainly mathematics
00:36:29.920 teachers that will say that people who do mathematics are very lucky because mathematics is the
00:36:36.320 one place where you can be sure that what you have found that the answer that you have found
00:36:42.880 is in fact absolutely 100% correct. But this is wrong. And the reason that is wrong is because
00:36:49.840 the mathematics has been done by a mathematician whose human and humans are always fallible.
00:36:55.440 The point is that the subject matter of mathematics is necessary truth. This is what David says
00:37:03.120 in the fabric of reality. So I'll say that again, the subject matter, what mathematics is studying
00:37:08.880 is necessary truth. But that's not the reward you get for doing mathematics as David.
00:37:15.120 It's much the same as in physics, the subject matter of physics is the laws of physics.
00:37:22.160 But that does not mean that by doing physics, we discover the final absolute laws of physics.
00:37:29.200 What we have is knowledge of the laws of physics. This is the crucial difference. It's not just
00:37:33.920 a quirky little bit of philosophy. This is an important thing to understand because it goes to the
00:37:38.800 heart of fallibility. That the knowledge of something is not the thing in itself. Here's my
00:37:46.800 tea cup. The tea cup is there. It's out there in the world in reality. I've got certain knowledge
00:37:53.040 about the tea cup, about how big it is, what color it is, and so on and so forth. I can be wrong
00:37:57.840 about any of that, even though the tea cup is right here in front of me, and I can provide a
00:38:01.840 description of it, which will necessarily always be incomplete and necessarily contain errors.
00:38:06.880 I can be wrong about any part of it. So too with mathematics. The mathematical realm is not
00:38:13.200 here in physical reality for us to look at, but it is there in abstract space. And we can be
00:38:18.960 wrong about the theorems of mathematics. We can prove theorems of mathematics, but those proofs,
00:38:24.960 the proof is just a certain kind of process, a computation that the mathematician goes through.
00:38:30.640 The computation does not confer on the conclusions of that computation. Upon the result of that
00:38:37.440 proof, absolute certainty. At any point in the proof, an error might have been committed,
00:38:45.360 an error might have crept in either because the mathematician themselves made an error.
00:38:50.080 There was an error in the assumptions of the calculator that was used to do the proof might have
00:38:54.320 been malfunctioning. There's any number of reasons why the conclusion of the proof might not
00:39:01.360 be absolutely true. And by the way, there are many mathematicians who do concede this pure
00:39:06.080 mathematician. So understand that the axioms they begin with. This is how mathematics works.
00:39:11.040 It begins with axioms. It follows rules of inference and so on. It leads to a conclusion.
00:39:15.680 The conclusion that can be regarded as a theorem. The point is that the axioms themselves,
00:39:22.000 even though they might be so-called self-evident, that itself does not confer absolute truth
00:39:30.880 upon the axioms. Self-evident to you could not be self-evident to someone else.
00:39:37.120 Whatever the case, you can't prove axioms are true. That's why they're called axioms.
00:39:42.960 But the conclusion in a valid proof only contains as much truth as the premises that you begin
00:39:49.600 with. How much truth there is in the assumptions is via the method of proof,
00:39:55.280 conferred upon the conclusion. But if you don't know how much truth is actually in the assumptions,
00:40:00.000 then you cannot possibly be certain of the absolute truth of your conclusion.
00:40:06.560 That's part of the mathematicians' misconception, as David speaks about in various
00:40:12.560 of the places. The very interesting part of this philosophy, the philosophy of mathematics as well.
00:40:20.320 And very poorly subscribed to, I should say as well. People do still have the hierarchy
00:40:26.240 of knowledge that is spoken about in the fabric of reality, where mathematics is up here
00:40:31.040 as the highest form, this rarefied sphere of absolute certainty. And just below that is science,
00:40:37.440 where although you can't be certain, you can be nearly certain. You can be very, very sure
00:40:40.800 about what's going on in science. And then below that is philosophy, where it's all just mere
00:40:45.360 matters of opinion. That's the classical, misconceived view of knowledge. Of course, knowledge is
00:40:51.280 an interconnected web where you can be wrong about any particular part of it. And where sometimes
00:40:56.080 there are far better explanations in philosophy than there are in certain areas of science.
00:41:00.960 And so on. Okay, let's go back to the book. So I just said that our knowledge of mathematics
00:41:07.520 is not infallible. But if representative meals meant that mathematicians are, or somehow ought to be,
00:41:13.120 societies best judges a fairness, then he was simply mistaken. The National Academy of Sciences
00:41:18.880 panel that reported to Congress in 1948 included the mathematician and physicist John von Neumann.
00:41:25.040 And it decided that a rule invented by the statistician Joseph Adnehill,
00:41:29.840 which is the one in yesterday, is the most impartial between states. But the mathematicians,
00:41:34.320 Michelle Balinski and Peyton Young, have since concluded that it favors smaller states.
00:41:40.240 This illustrates again that different criteria of impartiality favor different
00:41:44.640 apportionment rules, and which of them is the right criterion cannot be determined by mathematics.
00:41:49.680 Indeed, if representative meals intended his complaint ironically, if you really meant
00:41:54.640 that mathematics alone could not possibly be causing injustice and that mathematics alone
00:41:58.480 could not cure it, then he was right. However, there is a mathematical discovery that has
00:42:03.680 changed forever, the nature of the importionment debate. We now know that the question for an
00:42:08.640 apportionment rule that is both proportional and free from paradoxes can never succeed.
00:42:14.880 Balinski and Young proved this in 1975. Balinski and Young's Theorem,
00:42:21.120 every apportionment rule that stays within quota suffers from the population paradox.
00:42:27.920 This powerful, no-go theorem explains the long string of historical values to solve the apportionment
00:42:34.400 problem. Never mind the various other conditions that may seem essential for an apportionment
00:42:38.160 to be fair. No apportionment rule can meet even the bare bones requirements of proportionality
00:42:42.960 and the avoidance of the population paradox. Balinski and Young also proved no-go Theorem's
00:42:47.360 involving other classic paradoxes. This work had much broader context in the apportionment problem.
00:42:52.640 During the 20th century, and especially following the Second World War, a consensus had emerged
00:42:56.720 among most political movements that the future welfare of humankind would depend on an increase
00:43:02.240 in society-wide, preferably worldwide, planning and decision-making. The Western consensus
00:43:08.080 differed from its totalitarian counterparts, in that it expected the object of the exercise
00:43:13.520 to be the satisfaction of individual citizens' preferences. So Western advocates of society-wide
00:43:19.600 planning were forced to address a fundamental question that totalitarians do not encounter.
00:43:25.040 When a society as a whole faces a choice and citizens differ in their preferences among the
00:43:30.160 options, which option is best for a society to choose. If people are unanimous, there is no problem,
00:43:35.840 but no need for a plan or either. If they are not, which option can be rationally defended as
00:43:40.800 being the will of the people? The option that society wants, and that raises a second question,
00:43:46.080 how should society organize its decision-making so that it does indeed choose the options that it
00:43:50.880 wants? These two questions had been present, at least implicitly, from the beginning of modern democracy.
00:43:56.800 For instance, the US Declaration of Independence and the US Constitution both speak of the right of
00:44:01.680 the people to do certain things such as remove governments. Now they became the central questions
00:44:07.760 of a branch of mathematical game theory known as social choice theory. Thus game theory,
00:44:14.640 formally an obscure and somewhat whimsical branch of mathematics was suddenly thrust into the
00:44:18.800 centre of human affairs, just as rocketry and nuclear physics had been. Many of the world's
00:44:22.960 finest mathematical minds, including von Neumann, rose to the challenge of developing the theory
00:44:27.760 to support the needs of the countless institutions of collective decision-making that were being set up.
00:44:33.280 They would create new mathematical tools, which, given what all the individuals in a society
00:44:38.400 want or need or prefer, would distill what a society wants to do, thus implementing the aspiration
00:44:44.640 of the will of the people. They would also determine what systems of voting and legislating
00:44:50.320 would give society what it wants. Some interesting mathematics was discovered, but little,
00:44:55.600 if any of it, ever met those aspirations. On the contrary, time and again, the assumptions behind
00:45:02.160 social choice theory were proved to be incoherent or inconsistent by no-go theorems like that of
00:45:08.720 Belinsky and Young. Thus it turned out that the apportionment problem which had absorbed so much
00:45:13.440 legislative time, effort and passion was the tip of an iceberg. The problem is much less
00:45:20.640 parochial than it looks, for instance, rounding errors are proportionally smaller with a larger
00:45:26.560 legislature. So why don't they just make the legislature very big, say 10,000 members, so that all
00:45:32.240 the rounding areas would be trivial? One reason is that such a legislature would have to organize
00:45:37.840 itself internally to make any decisions. The factions within the legislature would themselves
00:45:42.320 have to choose leaders, policies, strategies and so on. Consequently, all the problems of social
00:45:47.360 choice would arise within the little society of a party's contingent in the legislature,
00:45:51.680 so it is not really about rounding errors. Also, it is not only about people's top preferences.
00:45:56.560 Once we are considering the details of decision-making in large groups, how legislatures and parties
00:46:02.480 infections within parties organize themselves to contribute their wishes to society's wishes,
00:46:07.760 we have to take into account their second and third choices. Because people still have a right
00:46:11.600 to contribute to decision-making if they cannot persuade a majority to agree to their first choice,
00:46:16.720 yet electoral systems designed to take such factors into account invariably introduce more paradoxes
00:46:23.440 and no-go theorems. One of the first no-go theorems was proved in 1951 by the economist
00:46:29.200 Kenneth Arrow, and it contributed to his winning the Nobel Prize for Economics in 1972.
00:46:34.480 Arrow's theorem appears to deny the very existence of social choice and to strike at the
00:46:39.280 principle of representative government and apportionment and democracy itself, and a lot more
00:46:43.280 besides. Pause it as my reflection. Just on this thing about Arrow's theorem, which we're about
00:46:48.080 to get to a description of, there's an interesting person on Twitter. Ethan the Mathemo,
00:46:54.720 he calls himself. He's got almost no followers. He's got 114 followers. He studies mathematics
00:47:02.800 at Cambridge. I don't know him personally at all. All I know is the articles that he writes for
00:47:10.160 medium.com, and they are remarkable explanations of mathematical theorems, and one of his most recent
00:47:17.840 ones is titled Proving Arrow's Impossibleity Theorem. If you want more details about Arrow's
00:47:25.040 theorem, go to medium.com, that type in Proving Arrow's Impossibleity Theorem, and Ethan, I believe,
00:47:34.560 is the fellow's name, has done a very comprehensive job of explaining the details of the proof.
00:47:44.400 I love this kind of thing. I did, you know, mathematics myself at university into including some
00:47:52.240 graduate level stuff, but I was never, I never had it myself as particularly good at it. So, for
00:47:59.440 example, I really, really wanted to know girdles and completeness theorem. I really wanted to
00:48:04.400 understand that and I took subjects at the higher undergraduate level in logic and computer
00:48:09.200 ability, and we went through the proof in great detail, but the only way I could ever get through
00:48:13.840 the proof was to buy a book, a companion, to go along with the proof as we did it, which
00:48:21.920 explained some more of the details. In fact, I have the book. It's a book about girdles proof. So,
00:48:33.760 an entire book written that explains girdles proof, I should say. It's not merely about the history
00:48:39.920 or anything like that. It's simply an explanation of girdles proof, what the mechanics of getting
00:48:45.440 through the damn proof are, because it's a very long proof all the time. Anyway, whatever the case,
00:48:51.680 this fellow on medium writes these similar, similarly easy to follow expositions of these
00:49:00.720 otherwise complicated mathematical proofs. Okay, let's go back to the book. David writes,
00:49:07.680 this is what Arrow did. He first laid down five elementary axioms that any rule defining
00:49:13.200 the will of the people, the preference of the preferences of a group, should satisfy.
00:49:18.160 And these axioms seem, at first sight, so reasonable as to be hardly worth stating.
00:49:24.400 One of them is that the rule should define our group's preferences only in terms of the
00:49:28.480 preferences of that group's members. Okay, same simple. Keep going. Another is that the rule
00:49:35.280 must not simply designate the rules of one particular person to be the preferences of the group
00:49:40.560 regardless of what the others want. This is called the no dictator axiom. A third is that if the
00:49:47.040 members of the group are unanimous about something, in the sense that they have all identical
00:49:51.040 preferences about it, then the rule must deem the group to have those preferences as well.
00:49:55.600 Those three axioms are all expressions in this situation of the principle of representative
00:50:00.080 government. Great. So they seem, as David has said, hardly even worth stating. They're so
00:50:06.960 blindingly obvious that if you have a group, it should be the preferences of the people in the
00:50:13.760 group, if it's a democratic type exercise that we're going through here in decision making.
00:50:20.240 It's the preferences of the group that dictate what the group is going to do. Not another group
00:50:25.360 over here that's dictating it. Okay, so or it's also not the case that one person from within
00:50:31.120 the group can dictate what the entire group can do. That's the no dictator rule. So let's keep going.
00:50:35.680 Arrow's fourth axiom is this. Suppose that under a different definition of the preferences of
00:50:41.200 the group, the rule deems the group to have a particular preference. Say for pizza over hamburger.
00:50:47.200 Then it must still deem that to be the group's preference. If some members who previously
00:50:51.760 disagreed with the group, i.e. they preferred hamburger to change their minds and now prefer pizza.
00:50:57.920 This constraint is similar to ruling out a population paradox. A group would be irrational
00:51:03.040 if it changed its mind in the opposite direction to its members. Again, simple straightforward stuff.
00:51:12.080 David continues. The last axiom is that if the group has some preference and then some members
00:51:17.120 change their minds about something else, then the rule must continue to assign the group
00:51:22.160 that original preference. For instance, if some members have changed their minds about the
00:51:25.760 relative merits of strawberries and raspberries, but none of their preferences about the relative
00:51:29.840 merits of pizza and hamburger have changed, then the group's preference between pizza and hamburger
00:51:34.560 must not be deemed to have changed either. This constraint can be again regarded as a matter
00:51:39.680 of rationality. If no members of the group change any of their opinions about a particular comparison,
00:51:44.160 nor can the group. All right, all simple axioms, very rational, straightforward ideas that it
00:51:53.680 would seem no rational person would want to disagree with. So what's the point? As David writes,
00:52:00.720 Arrow proved that the axioms that I have just listed are, despite their reasonable appearance,
00:52:05.920 logically inconsistent with each other. No way of conceiving the will of the people can satisfy
00:52:10.720 all five of them. This strikes at the assumptions behind social choice theory at an arguably
00:52:16.240 even deeper level than the theorems of Balinski and Young. First, Arrow's axioms are not about
00:52:21.600 the apparently parochial issue of apportionment, but about any situation in which we want to
00:52:26.080 conceive of a group as having preferences. Second, all five of these axioms are intuitively not
00:52:31.840 just desirable to make a system fair, but essential for it to be rational, yet inconsistent.
00:52:38.160 Pause their, just my commentary. How can you be rational yet inconsistent? Well,
00:52:43.280 this is a matter of logic as well, and it is reminiscent of girls in completeness theorem, by the way.
00:52:50.720 What is girls in completeness theorem? Well, firstly, let's consider a completeness theorem.
00:52:55.040 In this different kinds of logic, let's not go too much into the details. The simplest kind of
00:53:01.040 logic is centencial logic. It's very simple logic, okay, baby sort of logic. And you can prove
00:53:09.440 that everything is provable within that system of logic is true, and that every theorem that
00:53:15.360 you write down, every true statement that you can write down, true by according to the axioms right
00:53:20.640 of the logic, that everything that you can write down that is true also has a proof.
00:53:26.960 Now, this idea that everything you can prove is true is called soundiness, soundiness,
00:53:34.320 and everything that is true has a proof is called completeness. And this is true for
00:53:39.840 centencial logic, for the simplest of all logic. And I think the Kurt Gurdle, I'd have to look
00:53:45.040 this up, don't quote me on this, I think that maybe he's PhD thesis or something, that he proved
00:53:52.720 the completeness of predicate logic, which is slightly more complicated than centencial logic.
00:53:58.800 So predicate logic is just a little bit more complicated. It includes operators like
00:54:05.440 there exists a number x or for all x and so on, okay, that might get into the details.
00:54:12.480 The incompleteness theorem, the incompleteness theorem was a profound discovery.
00:54:18.320 It was about simple arithmetic. Now simple arithmetic, you know, 1 plus 2 equals 3 and so on,
00:54:25.360 simple arithmetic, we know what that is, is a more complicated system than basic logic,
00:54:29.840 the most basic forms of logic, the most basic forms of logic don't refer to numbers at all,
00:54:33.680 okay, but simple arithmetic obviously does. It's more complicated. It's richer.
00:54:37.680 What Kurt Gurdle proved was that although everything that you can prove within the system of
00:54:45.680 simple arithmetic and the system of simple arithmetic that he used was something that relied upon
00:54:51.680 Pino's axioms. This guy, Pino, came up with the axioms of simple arithmetic. Anyway,
00:54:57.120 everything that you can prove within that system was true according to that system.
00:55:01.440 But here's the kicker. He also proved, but he showed, this is the real profound discovery,
00:55:10.560 that you can write down true statements or at least statements and valid statements in the
00:55:17.040 system of simple arithmetic that have no proof. We cannot show that they are either true or false,
00:55:24.880 they're undecidable. This is profoundly strange and unusual. It means that there are things
00:55:30.880 in mathematics that are valid to write down, but for which we have no proof. We cannot show that
00:55:36.880 they're true or false mathematical understanding of those terms. That's what this here is reminiscent
00:55:42.880 of. We can have a sequence of perfectly reasonable axioms, just like the perfectly seemingly
00:55:52.800 perfectly reasonable axioms of simple arithmetic, Pino's axioms, which nonetheless can lead to
00:55:58.720 statements that cannot be proved true or false. We can't find a true or false proof of them.
00:56:06.400 They're undecidable, even though the axioms are so simple. So to hear, the axioms are
00:56:14.160 not only desirable, but essential for it to be rational, yet they are inconsistent and they
00:56:18.720 have a continuous. It seems to follow that a group of people jointly making decisions is necessarily
00:56:23.520 rational in one way or another. It may be a dictatorship or under some sort of arbitrary rule,
00:56:29.280 or if it meets all three representative conditions, then it must sometimes change its mind in a
00:56:33.760 direction opposite to that in which criticism and persuasion have been effective. So it will make
00:56:38.400 perverse choices no matter how wide and benevolent the people who interpret and enforce its preferences
00:56:43.600 may be. Unless, possibly, one of them is a dictator. So there is no such thing as the will of the
00:56:49.680 people. There is no way to regard society as a decision maker with self-consistent preferences.
00:56:55.840 This is hardly the conclusion that social choice theory was supposed to report back to the world.
00:57:02.320 As with the important problem, there were attempts to fix the implications of
00:57:06.240 arrows theorem with one out they just, ideas. For instance, one not take into account how intense
00:57:12.640 people's preferences are. For a slightly over half the electorate barely prefers x to y,
00:57:18.720 but the rest consider it a matter of life and death that y should be done.
00:57:23.360 Then most intuitive conceptions of representative government would designate y as the will of the
00:57:27.440 people. But intensities of preferences, and especially the differences in intensities among different
00:57:32.480 people, or between the same person at different times, and notoriously difficult to define
00:57:37.040 that alone measure, like happiness. We talked about that in the last chapter, of course.
00:57:41.520 So this idea that I feel really intensely about this particular thing, and you don't feel so
00:57:45.920 intense. So therefore my intensity of feeling should carry more weight than what yours does.
00:57:50.880 Well, how do you measure that? It's just self-reported again, but begs the question of the last
00:57:56.480 chapter. Okay, continuing. And in any case, including such things makes no difference. There are
00:58:03.120 still no go-theorems. Okay, I'm skipping just a little here, and we get into a very interesting thing
00:58:09.760 on which David has produced a video, in fact. So if you get a David Deutsches... In fact,
00:58:16.400 I'll link to David Deutsches video about this thing here, electoral systems. The electoral system
00:58:25.600 in Great Britain was proposed that people were suggesting and agitating and still do agitate,
00:58:33.200 as they do in Australian various other places, for changing the voting system.
00:58:38.160 It's an important problem. Given what else is being said in this chapter about how to rationally
00:58:43.760 make decisions, there can be better and worse ways of making decisions, better and worse ways of
00:58:49.440 having voting systems. Okay, and David writes on this topic. One perennially controversial
00:58:55.120 social choice problem is that of devising an electoral system. Such a system is mathematically
00:59:00.480 similar to an apportionment scheme, but instead of allocating seats to states on the basis of
00:59:05.520 population, it allocates them to candidates or parties on the basis of votes. However, it is more
00:59:11.600 paradoxical than apportionment and has more serious consequences, because in the case of elections,
00:59:17.440 the element of persuasion is central to the whole exercise. An election is supposed to determine
00:59:22.720 what the voters have become persuaded of. In contrast, apportionment is not about state trying to
00:59:28.480 persuade people to migrate from other states. Consequently, an electoral system can contribute to
00:59:34.160 or can inhibit traditions of criticism in this society concerned. Okay, so just my commentary. So
00:59:40.480 that's extremely important. If we want progress to continue as fast as possible, we need to ensure
00:59:47.680 that the traditions of criticism are not thwarted, but as David is saying here, there can be
00:59:55.040 the voting system which may inhibit traditions of criticism. And so it can actively stifle
1:00:00.800 progress, enabling society to solve problems as quickly as possible. Let's continue.
1:00:08.160 Any rights? For example, an electoral system in which seats are allocated wholly, or partly,
1:00:13.280 in proportion to the number of votes received by each party is called a proportional representation
1:00:18.560 system. We know from Belinsky and Young that if an electoral system is too proportional,
1:00:23.760 it will be subject to the analog of the population paradox and other paradoxes. And indeed,
1:00:28.240 the political scientist Peter Curid Clickgad in a study of the most recent eight general
1:00:33.680 elections in Denmark under its proportional representation system showed that every one of them
1:00:39.120 manifested paradoxes. These included the more preferred, less seats paradox in which a majority
1:00:45.120 of voters prefer party X to party Y, but party Y receives more seats than party X. But that is really
1:00:52.400 the least of the irrational attributes of proportional representation. A more important one,
1:00:56.800 which is shared by even the mildest of proportional systems, is that they assign
1:01:01.120 disproportionate power in the legislature to the third largest party. And often to even smaller
1:01:08.320 parties. It works like this. It is rare in any system for a single party to receive an overall
1:01:13.840 majority of votes. Hence, if votes are reflected proportionally in the legislature, no legislation
1:01:19.280 can be passed unless some of the parties cooperate to pass it. And no government can be formed
1:01:23.920 unless some of them form a coalition. Sometimes the two largest parties manage to do this,
1:01:28.480 but the most common outcome is that the leader of the third largest party holds the balance of
1:01:33.680 power and decides which of the two largest parties shall join it in government and which
1:01:38.640 shall be sidelined and for how long. That means that it is correspondingly harder for the
1:01:43.680 electorate to decide which party and which policies will be removed from power,
1:01:47.840 pause their moral reflection. This is a very common problem in Australia. We do have
1:01:55.920 large minority parties, by which I meet third parties. Basically in Australia we have
1:02:02.960 two main parties, the Labor Party and the Liberal Party. Or in federal it is the Liberal Coalition
1:02:10.000 Party, which is a neat way of getting around the fact that the Liberal Party has formed a
1:02:14.960 coalition with the national party. And so it's the Liberal National Coalition. And so already we
1:02:20.720 have a bit of an issue there, which results in compromise and everything else that we were talking
1:02:25.360 about earlier. But the Greens have, over the years, been a sizeable third party. And in some
1:02:35.120 places in certain states, the Greens have become large enough to sometimes ally themselves with
1:02:40.880 Labor, with the Labor Party, with the left side. And so then the two of them together can form
1:02:48.160 a coalition, which is larger than the Liberal Party, which often is the largest party.
1:02:53.760 Or even worse than that, the green party will not form a coalition with anyone. It will just sit
1:02:59.040 in the middle and it will hold this balance of power. It's been a number of times over the
1:03:03.680 years where in the Senate in Australia, the green party has held that balance of power.
1:03:08.800 Which means it, although it might only have two, three senators out of the 76 that are actually
1:03:15.680 in the Parliament of Australia, might only have two or three, that is enough to either give
1:03:20.640 Labor a majority or the Liberal Party a majority. Which means then that in fact the most powerful
1:03:26.880 party, in a sense, is the green party because they become the Kingmakers. Now David, David goes
1:03:33.280 through a historic example here about West Germany, where in fact the green, the green center
1:03:39.360 like being the third party, changing sides in Germany. So I'll just skip that a little bit
1:03:46.480 and I'll go back to the book where David writes,
1:03:48.880 Arrow's theorem applies not only to collective decision-making, but also to individuals as follows.
1:03:54.800 Consider a single rational person faced with a choice between several options
1:03:59.520 if the decision requires thought, then each option must be associated with an explanation,
1:04:05.040 at least a tentative one for White might be best, to choose an option as to choose the explanation.
1:04:10.240 So how does one decide which explanation to adopt? Common sense says that one weighs them,
1:04:17.040 or weighs the evidence that their arguments present. This is an ancient metaphor,
1:04:22.080 statues of justice have carried scale since antiquity. More recently inductiveism has cast
1:04:26.800 scientific thinking in the same mould, saying that scientific theories are chosen, justified and
1:04:32.080 believed, and somehow even formed in the first place according to the weight of evidence in their
1:04:36.240 favour. Just my commentary there, that Bayesianism as well, Bayesianism tries to mathematize
1:04:44.320 this idea of inductivism as being about weighing the evidence in order to decide which theory
1:04:52.080 is correct, or even, as the Bayesians will say, to produce the theory in the first place.
1:04:57.840 But the critical rationalist understanding is that theories are creatively conjectured,
1:05:03.600 and the function of evidence is to simply decide between them. It's a black and white process.
1:05:08.080 It's not a matter of weighing that the evidence will actually rule out all the theories,
1:05:12.320 except for one, and the evidence then is explained by that single remaining theory.
1:05:18.720 For example, again, going back to Edenton's experiment in 1919, which decided between
1:05:26.480 Newton's theory of gravity and Einstein's theory of gravity, and it ruled out Newton's theory
1:05:32.000 of gravity, and in fact all other theories of gravity. And the observations that were made,
1:05:36.480 the evidence that was seen, was explained by general relativity. That's the way of understanding
1:05:41.280 the philosophy of science. There's poppers, way of explaining this, that is David Deutsch's way
1:05:46.320 of explaining this. This is the correct way of explaining this. What Bayes would say is that somehow
1:05:50.880 are the way of the evidence. And one way of just refuting Bayes, my own personal way of refuting
1:05:57.120 Bayes, is that in 1919 almost every physicist will agree that the experiment was a crucial experiment
1:06:03.600 which ruled out Newton in favor of Einstein. But if you are really a committed Bayesian,
1:06:09.680 shouldn't you regard that all the experiments prior to 1919, that almost all the many hundreds
1:06:17.840 or thousands of experiments that have been done, observations that have been made,
1:06:21.920 that were consistent with Newton's theory of gravity? Shouldn't they count on the scales,
1:06:28.880 and so you've got all of this weight of evidence from Newton weighing down one side,
1:06:33.520 and apparently you only have one experiment here with regard to Einstein, and so shouldn't
1:06:37.920 Newton still be regarded as true on Bayes' theorem? Well of course the Bayesians then have,
1:06:42.320 I guess they would do this little dance where they would say, oh no but Einstein's theory now
1:06:47.280 subsumes all of that previous evidence that was counted for Newton. Well that's kind of
1:06:53.360 a critical rationalist view. It's saying that indeed this experiment is the one that says that now
1:06:59.680 all of that other evidence is in fact explained best by the general theory of relativity and not
1:07:05.200 by Newton's theory of gravity. So the Bayesian I presume would collapse into being a critical
1:07:10.160 rationalist at that point, although I'm being unfair to the Bayesians because I don't have one
1:07:14.800 here and I'm not planning on interviewing one either. Okay back to the book. When we're talking
1:07:21.520 about weight of evidence David writes, consider that supposed weighing process. Each piece of
1:07:27.920 evidence including each feeling, prejudice, value, axiom, argument and so on, depending upon what
1:07:32.880 weight it had in that person's mind would contribute that amount to that person's preferences
1:07:38.320 between various explanations. Hence for the purposes of arrows theorem each piece of evidence can
1:07:42.880 be regarded as an individual participating in the decision making process where the person as a whole
1:07:48.880 would be the group. Now the process that adjudicates between the different explanations would have
1:07:52.800 to satisfy certain constraints if it were to be rational. For instance if having decided that one
1:07:58.800 option was the best that the person received further evidence that gave additional weight to that
1:08:04.720 option then the person's overall preference would still have to be for that option and so on.
1:08:10.240 Arrow's theorem says that those requirements are inconsistent with each other and so seem to imply
1:08:14.640 that all decision making or thinking must be irrational. Unless perhaps one of the internal
1:08:20.640 agencies is dictator in power to override the combined opinions of all the other agents but this
1:08:25.280 is an infinite regress. How does the dictator itself choose between rival explanations about which
1:08:30.480 other agents it would be best to override and here we get to the real gold nugget the center of this
1:08:36.880 chapter and David writes, there is something very wrong with that entire conventional model of
1:08:43.040 decision making both within single minds and for groups as assumed in social choice theory.
1:08:48.960 It consists of decision making as a process of selecting from existing options according to a
1:08:53.840 fixed formula such as an apportionment rule or electoral system but in fact that is only what happens
1:08:59.040 at the end of decision making the phase that does not require creative thought in terms of
1:09:04.320 Edison's metaphor the model refers only to the perspiration phase without realizing that decision
1:09:09.840 making is problem solving and that without the inspiration phase nothing is ever solved and there
1:09:15.040 is nothing to choose between. At the heart of decision making is the creation of new options
1:09:20.000 and the abandonment or modification of existing ones to choose an option rationally is to choose
1:09:26.320 the associated explanation therefore rational decision making consists not of weighing evidence
1:09:31.760 but of explaining it in the course of explaining the world. One judges arguments as explanations
1:09:38.080 not just applications and one does this creatively using conjecture tempered by every kind of
1:09:43.120 criticism it is in the nature of good explanations being hard to vary that there is only one of them
1:09:49.360 having created it one is no longer tempted by the alternatives they have not been outweighed but
1:09:54.560 argued refuted and abandoned during the course of a creative process one is not struggling to
1:09:59.600 distinguish between countless different explanations of nearly a core merit typically one is
1:10:04.240 struggling to even create one good explanation and having succeeded one is glad to be read of the rest
1:10:10.640 wow okay so that really does go quite the distance to explaining what's wrong with conventional
1:10:21.680 ideas about decision making and what David Deutsch is presenting here that's putting creativity
1:10:28.320 at the center of how we go about choosing things moving on to the next part and this is where David
1:10:34.640 talks about compromise which is the way I began if you recall so let's get into David's explanation
1:10:40.480 of this another misconception to which the idea of decision making by weighing sometimes leads
1:10:46.560 is that problems can be solved by weighing in particular that disputes between advocates of
1:10:50.640 rival explanations can be resolved by creating a weighted average of their proposals but the fact is
1:10:56.080 that a good explanation being hard to vary at all without losing its explanatory power
1:11:00.320 is hard to mix with a rival explanation something halfway between them is usually worse than
1:11:05.040 either than separately mixing two explanations to create a better explanation requires an additional
1:11:10.560 act of creativity that is why good explanations are discrete separated from each other by bad
1:11:16.320 explanations and why when choosing between explanations we are faced with discrete options
1:11:21.200 pause their my reflection so this is precisely again I keep on going back to the same
1:11:26.320 trite example but it serves the purpose here if we have two theories Einstein's theory of
1:11:31.200 general relativity and and and and Newton's theory of gravity and Newton's theory of gravity is
1:11:37.680 basically summed up by the formula f equals gm1 m2 of r squared and Einstein's theory of relativity
1:11:44.000 is far more complicated mathematically but is about the curvature of spacetime if we weren't able
1:11:49.920 to decide between these two for some reason or other if we're at a point where just prior to
1:11:54.800 1919 we didn't have the crucial experiment just yet but it seemed like iron science theory was
1:11:59.920 making some good predictions consistent with what Newton's theory was the conventional model of
1:12:06.000 coming up with a compromise given that we couldn't decide between them perhaps if you're a
1:12:09.840 smart physicist that understands both you can't actually you're not in a position yet to decide
1:12:15.280 the idea that you can come up with a compromise something that's halfway between the two
1:12:19.680 is ridiculous one that's halfway but whatever that would mean to have the one that's halfway
1:12:24.640 between the two I don't know but if we could we would expect that there's a bad explanation
1:12:30.720 because here we have two good explanations two good explanations competing for explaining gravity
1:12:37.920 something that's halfway between won't be a good explanation whatever halfway between those two
1:12:41.600 means back to the book David writes in complex decisions the creative phases often followed by
1:12:46.480 mechanical perspiration phase in which one tires down details of the explanation that are not
1:12:51.440 yet hard to vary but can be made so by non-creative means for an example an architect whose client
1:12:57.280 asks how taller skyscraper can be built given certain constraints does not just calculate that
1:13:02.560 number from a formula the decision making process may end with such a calculation but it begins
1:13:07.840 creatively with ideas for how the client's priorities and constraints might best be met by new
1:13:13.360 design and before that the clients had to decide creatively what those priorities and constraints
1:13:19.680 should be at the beginning of that process they would not have been aware of all the preferences
1:13:24.560 they would end up presenting to the architects okay so I'm just skipping a little more here
1:13:30.720 and David compares that process to voting namely that the person is choosing between when when
1:13:38.400 voting a rational person is choosing between their explanations of politicians and their policies
1:13:44.480 they're not weighing things in their mind they're ruling out they're criticizing and abandoning
1:13:50.960 once and for all particular political parties or particular candidates that's how they choose between
1:13:56.720 people back to the book so it is not true that decision making necessarily suffers from those
1:14:03.600 crude or rationalities not because there is anything wrong with arrows theorem or in any of the
1:14:08.480 other no gothems but because social choice theory is itself based on false assumptions about what
1:14:16.320 thinking and deciding consist of it is Zeno's mistake it is mistaking an abstract process that
1:14:22.080 it has named decision making for the real life process of the same name so this is so important
1:14:29.360 in just pause their my commentary this is so important in science and philosophy that when someone
1:14:34.400 has named something and they say social choice theory and this is mathematics and this is the
1:14:40.640 mathematics that governs how people make choices just because they've named it that doesn't mean
1:14:47.280 that it actually is about how society makes choices they've just called it that one might very
1:14:54.000 well say the same for other subjects perhaps all of psychology it's because it's name psychology
1:15:00.720 what these people in academic psychology engaged in sometimes evolutionary psychology might not
1:15:06.640 actually be psychology it might not actually deserve the name this can happen more often than
1:15:14.160 we might appreciate or we might want to admit admit as well people name morality all sorts of
1:15:21.040 things as well and it's not actually morality just because you call up that doesn't mean that's
1:15:25.840 what you're actually studying that doesn't mean that that's what you're actually talking about
1:15:29.680 you just named it that thing you have mistake perhaps an abstract process that you're going through
1:15:36.240 that you have named in this case decision making for the real life process of the same name
1:15:40.960 okay skipping a little bit more and David then talks about what what people's reaction to these
1:15:47.840 no-go theorems has been the despite the fact that mathematics has been shown to reveal that
1:15:55.840 it's almost impossible to come up with consistent and rational means by which we can make decisions
1:16:03.360 or what's to be in response to that David writes virtually all commentators have responded to these
1:16:08.480 paradoxes no-go theorems in a mistaken and rather revealing way they regret them this illustrates
1:16:15.120 a confusion to which I am referring they wish that these theorems of pure mathematics were false
1:16:20.640 if only mathematics permitted it they complain we human beings could set up a just society
1:16:25.760 that makes its decisions rationally but faced with the impossibility of that there is nothing left
1:16:30.960 for us to do but to decide which injustices and irrationalities we like best and to
1:16:36.880 enshrine them in law as webster wrote of the important problem that which cannot be done perfectly
1:16:42.320 must be done in a matter as near perfection as can be if exactness cannot from the nature of
1:16:47.520 things be attained then the nearest practical approach to exactness ought to be made
1:16:51.680 but what sort of perfection is a logical contradiction a logical contradiction is nonsense the truth
1:16:57.760 is simpler if your conception of justice conflicts with the demands of logical rationality then it
1:17:03.120 is unjust if your conception of rationality conflicts with a mathematical theorem or in this case
1:17:09.040 with many theorems then your conception of rationality is irrational to stick stubbornly to
1:17:14.880 logically impossible values not only guarantees failure in the narrow sense that one can never
1:17:19.600 meet them it also forces one to reject optimism every evil is due to a lack of knowledge
1:17:25.520 and so deprives one of the means to make progress wishing for something that is logically
1:17:31.280 impossible is a sign that there is something better to wish for moreover if my conjecture in
1:17:36.560 chapter eight is true and impossible wish is ultimately uninteresting as well okay i've almost
1:17:42.240 finished the chapter but i'm gonna i'm gonna stop there actually for today because this one's
1:17:47.440 gone on for long enough it's only been a two-part episode all about choices but i hope you've
1:17:52.800 enjoyed this one i've found this one really fascinating i remember when i first read the book
1:17:57.680 when i encountered this chapter i thought it's a rather strange choice for David to make on choices
1:18:04.160 to talk about to spend so long talking about one particular parochial issue but it's clear in
1:18:12.240 retrospect why that was done to reveal that the supposedly perfectly logical rational systems
1:18:19.920 are not the only thing we need in reality to guide our behavior as human beings in our societies
1:18:27.280 mathematics is indispensable in many ways but is not the cure all nothing is the cure all
1:18:33.920 creativity will always be required and again this puts people at the center so much of actual
1:18:41.360 reality that we are guiding in a way the way in which the entire cosmos is evolving at the moment
1:18:48.640 only locally here on planet earth unless we're guiding the way in which the earth is kind of
1:18:53.840 terraforming itself constructing new things and we're doing that by making choices thank you for
1:19:01.040 listening i'll see you very soon again for the next chapter bye bye once more as always thank
1:19:07.280 you everyone for the support on patreon if you're interested in making a patreon regular donation
1:19:14.000 or a one-off donation you can search for me on google or there's a paypal account as well that's
1:19:21.200 useful for one-off donations thanks again and see you next time bye bye