The Beginning of Infinity: Explanations That Transform the World (59 page)

In contrast, the error-correcting attributes of the plurality voting system have a tendency to avoid the paradoxes to which the system is theoretically prone, and quickly to undo them when they do happen, because all those incentives are the other way round. For instance, in the Canadian province of Manitoba in 1926, the Conservative Party received more than twice as many votes as any other party, but won
none
of the seventeen seats allocated to that province. As a result it lost power in the national Parliament despite having received the most votes nationally too. And yet, even in that rare, extreme case, the disproportionateness between the two main parties’ representations in Parliament was not that great: the average Liberal voter received 1.31 times as many members of Parliament as the average Conservative one. And what happened next? In the following election the Conservative Party again had the largest number of votes nationally, but this time that gave it an overall majority in Parliament. Its vote had increased by 3 per cent of the electorate, but its representation had increased by 17 per cent of the total number of seats, bringing the parties’
shares of seats back into rough proportionality and satisfying Popper’s criterion with flying colours.

This is partly due to yet another beneficial feature of the plurality system, namely that elections are often very close, in terms of votes as well as in the sense that all members of the government are at serious risk of being removed. In proportional systems, elections are rarely close in either sense. What is the point of giving the party with the most votes the most seats, if the party with the third-largest number of seats can then put the second-largest party in power regardless – there to enact a compromise platform that absolutely no one voted for? The plurality voting system almost always produces situations in which a small change in the vote produces a relatively large change (in the same direction!) in who forms a government. The more proportional a system is, the less sensitive the content of the resulting government and its policies are to changes in votes.

Unfortunately there are political phenomena that can violate Popper’s criterion even more strongly than bad electoral systems – for example, entrenched racial divisions, or various traditions of political violence. Hence I do not intend the above discussion of electoral systems to constitute a blanket endorsement of plurality voting as the One True System of democracy, suitable for all polities under all circumstances. Even democracy itself is unworkable under some circumstances. But in the advanced political cultures of the Enlightenment tradition the creation of knowledge can and should be paramount, and the idea that representative government depends on proportionate representation in the legislature is unequivocally a mistake.

In the United States’ system of government, the Senate is required to be representative in a different sense from the House of Representatives:
states
are represented equally, in recognition of the fact that each state is a separate political entity with its own distinctive political and legal tradition. Each of them is entitled to two Senate seats, regardless of population. Because the states differ greatly in their populations (currently the most populous state, California, has nearly seventy times the population of the least populous, Wyoming), the Senate’s apportionment rule creates enormous deviations from population-based proportionality – much larger than those that are so hotly disputed in regard to the House of Representatives. And yet
historically, after elections, it is rare for the Senate and the House of Representatives to be controlled by different parties. This suggests that there is more going on in this vast process of apportionments and elections than merely ‘representation’ – the mirroring of the population by the legislature. Could it be that the problem-solving that is promoted by the plurality voting system is continually changing the
options
of the voters, and also their
preferences
among the options, through persuasion? And so opinions and preferences are, despite appearances,
converging
– not in the sense of there being less disagreement (since solutions create new problems), but in the sense of creating ever more shared knowledge.

In science, we do not consider it surprising that a community of scientists with different initial hopes and expectations, continually in dispute about their rival theories, gradually come into near-unanimous agreement over a steady stream of issues (yet still continue to disagree all the time). It is not surprising because, in their case, there are observable facts that they can use to test their theories. They converge with each other on any given issue because they are all converging on the objective truth. In politics it is customary to be cynical about that sort of convergence being possible.

But that is a pessimistic view. Throughout the West, a great deal of philosophical knowledge that is nowadays taken for granted by almost everyone – say, that slavery is an abomination, or that women should be free to go out to work, or that autopsies should be legal, or that promotion in the armed forces should not depend on skin colour – was highly controversial only a matter of decades ago, and originally the opposite positions were taken for granted. A successful truth-seeking system works its way towards broad consensus or near-unanimity – the one state of public opinion that is not subject to decision-theoretic paradoxes and where ‘the will of the people’ makes sense. So convergence in the broad consensus over time is made possible by the fact that all concerned are gradually eliminating errors in their positions and converging on objective truths. Facilitating that process – by meeting Popper’s criterion as well as possible – is more important than which of two contending factions with near-equal support gets its way at a particular election.

In regard to the apportionment issue too, since the United States’
Constitution was instituted there have been enormous changes in the prevailing conception of what it means for a government to be ‘representative’. Recognizing the right of women to vote, for instance, doubled the number of voters – and implicitly admitted that in every previous election half the population had been disenfranchised, and the other half over-represented compared with a just representation. In numerical terms, such injustices dwarf all the injustices of apportionment that have absorbed so much political energy over the centuries. But it is to the credit of the political system, and of the people of the United States and of the West in general, that, while they were fiercely debating the fairness of shifting a few percentage points’ worth of representation between one state and another, they were also debating, and making, these momentous improvements. And they too became uncontroversial.

Apportionment systems, electoral systems and other institutions of human cooperation were for the most part designed, or evolved, to cope with day-to-day controversy, to cobble together ways of proceeding without violence despite intense disagreement about what would be best. And the best of them succeed as well as they do because they have, often unintentionally, implemented solutions with enormous reach. Consequently, coping with controversy in the present has become merely a means to an end. The purpose of deferring to the majority in democratic systems should be to approach unanimity in the future, by giving all concerned the incentive to abandon bad ideas and to conjecture better ones. Creatively
changing the options
is what allows people in real life to cooperate in ways that no-go theorems seem to say are impossible; and it is what allows individual minds to choose at all.

The growth of the body of knowledge about which there is unanimous agreement does not entail a dying-down of controversy: on the contrary, human beings will never disagree any less than they do now, and that is a very good thing. If those institutions do, as they seem to, fulfil the hope that it is possible for changes to be for the better, on balance, then human life can improve without limit as we advance from misconception to ever better misconception.

Representative government
   A system of government in which the composition or opinions of the legislature reflect those of the people.

Social-choice theory
   The study of how the ‘will of society’ can be defined in terms of the wishes of its members, and of what social institutions can cause society to enact its will, thus defined.

Popper’s criterion
   Good political institutions are those that make it as easy as possible to detect whether a ruler or policy is a mistake, and to remove rulers or policies without violence when they are.

– Choice that involves creating new options rather than weighing existing ones.

– Political institutions that meet Popper’s criterion.

It is a mistake to conceive of choice and decision-making as a process of selecting from existing options according to a fixed formula. That omits the most important element of decision-making, namely the creation of new options. Good policies are hard to vary, and therefore conflicting policies are discrete and cannot be arbitrarily mixed. Just as rational thinking does not consist of weighing the justifications of rival theories, but of using conjecture and criticism to seek the best explanation, so coalition governments are not a desirable objective of electoral systems. They should be judged by Popper’s criterion of how easy they make it to remove bad rulers and bad policies. That designates the plurality voting system as best in the case of advanced political cultures.

My daughter Juliet, then aged six . . . pointed out some flowers by the wayside. I asked her what she thought wildflowers were for. She gave a rather thoughtful answer. ‘Two things,’ she said. ‘To make the world pretty, and to help the bees make honey for us.’ I was touched by this and sorry I had to tell her that it wasn’t true.

Richard Dawkins,
Climbing Mount Improbable
(1996)

‘Displace one note and there would be diminishment. Displace one phrase and the structure would fall.’ That is how Mozart’s music is described in Peter Shaffer’s 1979 play
Amadeus
. This is reminiscent of the remark by John Archibald Wheeler with which this book begins, speaking of a hoped-for unified theory of fundamental physics: ‘an idea so simple, so beautiful, that when we grasp it . . . how could it have been otherwise?’

Shaffer and Wheeler were describing the same attribute: being hard to vary while still doing the job. In the first case it is an attribute of aesthetically good music, and in the second of good scientific explanations. And Wheeler speaks of the scientific theory as being
beautiful
in the same breath as describing it as hard to vary.

Scientific theories are hard to vary because they correspond closely with an objective truth, which is independent of our culture, our personal preferences and our biological make-up. But what made Peter Shaffer think that Mozart’s music is hard to vary? The prevailing view among both artists and non-artists is, I think, that there is nothing objective about artistic standards. Beauty, says the adage, is in the
eye of the beholder. The very phrase ‘It’s a matter of taste’ is used interchangeably with ‘There is no objective truth of the matter.’ Artistic standards are, in this view, nothing more than artefacts of fashion and other cultural accidents, or of individual whim, or of biological predisposition. Many are willing to concede that in science and mathematics one idea can be objectively truer than another (though, as we have seen, some deny even that), but most insist that there is no such thing as one object being objectively more beautiful than another. Mathematics has its proofs (so the argument goes), and science has its experimental tests; but if you choose to believe that Mozart was an inept and cacophonous composer then neither logic nor experiment nor anything else objective will ever contradict you.

However, it would be a mistake to dismiss the possibility of objective beauty for that sort of reason, for it is none other than the relic of empiricism that I discussed in
Chapter 9
– the assertion that philosophical knowledge in general cannot exist. It is true that, just as one cannot
deduce
moral maxims from scientific theories, likewise nor can one deduce aesthetic values. But that would not prevent aesthetic truths from being linked to physical facts through explanations, as moral ones are. Wheeler was very nearly asserting such a link in that quotation.

Facts can be used to criticize aesthetic theories, as they can moral theories. For instance, there is the criticism that, since most arts depend on parochial properties of human senses (such as which range of colours and sounds they can detect), they cannot be attaining anything objective. Extraterrestrial people whose senses detected radio waves but not light or sound would have art that was inaccessible to us, and vice versa. And the reply to that criticism might be, first, that perhaps our arts are merely scratching the surface of what is possible: they are indeed parochial, but they are a first approximation to something universal. Or, second, that deaf composers on Earth have composed, and appreciated, great music; why could deaf extraterrestrials (or humans who were born deaf) not learn to do the same – if by no other means than by downloading a set of deaf-composer aesthetics into their brains? Or, third, what is the difference between using radio telescopes to understand the physics of quasars and using prosthetic senses (wired into the brain to create new qualia) to appreciate extraterrestrial art?

Experience may also provide artistic
problems
. Our ancestors had eyes and paint, which may have led them to wonder how paint could be used in a way that would look more beautiful.

Just as Bronowski pointed out that scientific discovery depends on a commitment to certain moral values, might it not also entail the appreciation of certain forms of beauty? It is a fact – often mentioned but seldom explained – that deep truth is often beautiful. Mathematicians and theoretical scientists call this form of beauty ‘elegance’. Elegance is the beauty in explanations. It is by no means synonymous with how good, or how true, an explanation is. The poet John Keats’ assertion (which I think was ironic) that ‘Beauty is truth, truth beauty’ is refuted by what the evolutionist Thomas Huxley called ‘the great tragedy of Science – the slaying of a beautiful hypothesis by an ugly fact – which is so constantly being enacted under the eyes of philosophers’. (By ‘philosophers’ he meant ‘scientists’.) I think Huxley, too was being ironic in calling this process a great tragedy, especially since he was referring to the refutation of spontaneous-generation theories. But it is true that some important mathematical proofs, and some scientific theories, are far from elegant. Yet the truth so often
is
elegant that elegance is, at least, a useful heuristic when searching for fundamental truths. And when a ‘beautiful hypothesis’ is slain, it is more often than not replaced, as the spontaneous-generation theory was, by a more beautiful one. Surely this is not coincidence: it is a regularity in nature. So it must have an explanation.