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Yes, OP no good.

Seriously though, I think your assumptions are a bit much. Reading through the bit on bias, that people ought to be unbiased estimators of their own judgement, I thought of that line that runs something like 95% of professors believe they're in the top 5% of good teachers, or something like that. I don't think people are necessarily good judges of themselves, and I'm not sure if that's an issue of either rationality or morality as much as perception and perspective.

Really, should anybody vote at all? After all, we all know what the result would be. We can all just act as if somebody voted. :)

I should say that I am basing my comment on Aumann via Wikipedia, not on Nick's argument. :)

Well, there are the terrible, unsupported and downright egregious assumptions and conclusions that the post contains, but I will demolish those shortly.

Otherwise it was perfectly entertaining.

First point. There is no such thing as absolute truth in politics. This is because we do not and cannot know all things, most especially the future. Define "morally right". That's a PhD in an of itself, right there. In economics we can do a lot with a few given assumptions or axioms, things which are defined, do not need to be proved, and we proceed from. In politics we attack assumptions and axioms with gleeful abandon.

Second point. As mentioned in the wiki article, no two people have the same priors. A prior in this case is the sum total of their life experiences, circumstances and personality. These are what informs a voters' judgment and choice every time they vote. Therefore just on this point Aumann is out the window.

So we change the point. We have a process to allow us as a society to make choices and a method to present those choices to the people. That's an election. It's all about the process enabling us to gather the information on what the public wants by electing the leaders it wants. In politics we call this getting a mandate. See the Second Labour Government in 1945 Britain for the poster-child definition of this result.

Sorry about the smouldering pile of ash that I reduced your argument to Nick. Shall I get the broom?

Dunno Jim. Thinking through history, I would say that some of the most evil people are those who overestimate the rightness of their own cause. So go to any means to promote it. And obeying the rules of a democracy means we recognise some moral validity of others' judgements, even when they differ from our own. I'm just pushing that argument to its logical (absurd?) conclusion.

Determinant: "First point. There is no such thing as absolute truth in politics. This is because we do not and cannot know all things, most especially the future."

That assumption of uncertainty is central to my argument. That's why I defined "judgement" as "probability of voting for the right party or policy".

"Second point. As mentioned in the wiki article, no two people have the same priors."

That's where Robin Hanson comes in. Read on down the wiki.

OK, here is a thought about Nick's argument.

Suppose that I believe, correctly, that my judgement is better than anyone else's, but I am still fallible, and I know that my judgement is not perfect on the matter in question. Why should I cast the only vote? Perhaps the thing to do is for everybody to cast a vote and weight each vote according to the voter's judgement. In that case my vote may count for more than anyone else's, but the decision does not rest upon the frail reed of my imperfect judgement.

Min: if we were estimating the number of beans in a jar, your argument would be correct. That's the wisdom of crowds argument. We pool people's judgement, just like we pool samples. (And we weight the samples or votes if some samples or judgements are better than others). But here it's not a case where we can take a weighted average of the votes, to pool the wisdom. It's party A or B. I'm not 100% sure, but I think the optimum weights are 0% 100%.

That assumption doesn't save you. You can't define "right" objectively.

Commented on the other thread before seeing this one. May repeat here...

I read the Hanson abstract but no access to gated article. But I would guess that the argument requires fairly strong conditions on the prior, ie wavefunction of the universe. I assume, of course, that you have knowledge the true physics of the universe. But even then, the subject cannot, even in principle perform a quantum measurement to determine his own state. I could carry an experiment to take determine the state of you, and you could subsequently carry out an experiment to determine the state of me. But the system as a whole cannot know the state of the whole system. One part must necessarily be isolated to measure, record, and compute the result of observation. And two observers can never bring their state models into coherence without interfering with the observed states.

And in practice, the space of the prior (all possible states of the universe consistent with all possible physics) is so unimaginably huge, that we cannot even begin to quantify the size or shape of it. So in principle, and especially in practice, it is perfectly reasonable for "rational" humans to disagree.

Finally, we still have to be altruistic to elect a dictator. Just because we're rational doesn't mean we have the same preferences. I, for example, prefer to have more stuff than you. Your preferences may differ.

Is this a product of first past the post? Does single transferable vote help? I'm too tired to try to work it out just now.

Parties in particular are a mish-mash of policies. And people have a mish-mash of different preferences. If we relax the constraint of 'right party' or 'right policy' and admit that there isn't always a right or wrong policy, then people voting isn't immoral or irrational, it's just selfish (maybe that immoral ... I dunno).

Imagine an electorate of 2 people (A and B) and two parties: the Free Chocolate Ice Cream Party and the Free Vanilla Ice Cream Party. A likes chocolate. B like vanilla. Guaranteed coalition! Neither will ever agree to sit out the vote.

Suppose that there are three potential voters, A, B, and C. The probability that A will vote correctly is 3/4, and the probability that each of B or C will vote correctly is 2/3, all probabilities being independent. Then a majority vote of the three will be better than simply relying upon the vote of A.

The probability that all three will vote correctly is 1/3.
The probability that A and B will vote correctly and C will vote incorrectly is 1/6.
The probability that A and C will vote correctly and B will vote incorrectly is 1/6.
The probability that A will vote incorrectly and B and C will vote correctly is 1/9.

The probability that the majority will vote correctly is 7/9, which is greater than 3/4.

People vote in order to express their preferences in the same that they purchase goods in order to express their preferences.

Do you want to build a public swimming pool? Some like to swim. Others prefer lower taxes. They hold a vote.

And you cannot say that there is an objective social welfare maximizing outcome that can be determined other than by voting, because how else do we obtain this information? We could take a poll, and then run a simulation, but that is not too far from voting.

Very entertaining argument. Of course, by Aumann's Agreement Theorem, all rational voters will agree on the candidate to vote for, so it doesn't matter which of them votes. But then, you're assuming variation in judgement, which contradicts the assumptions required for Aumann's Theorem to hold (that is, perfect bayesian reasoning with communicable evidence).

Suppose our plebiscite is intended to answer a yes/no question for which there is an objective best answer upon which we would all agree with full knowledge. This addresses RSJ's (excellent) objection.

Suppose each of us has a noisy signal. From our imaginations and experience we form a conjecture, which for each of us is true with probability p (and therefore false with probability 1-p). We assume that p > 0.5, and that our conjectures are independent.

By assumption, we cannot rank judgment in this setup. (We all have the same judgment.) The best way to ensure a good answer is if everyone votes. Since p > 0.5, the likelihood of error goes to zero as the number of voters grows large, but may be high for a small number of voters. This is a "wisdom of crowds" argument, but it is not ruled out for a yes/no question.

(Note that our decision rule is majority wins, which is equivalent to averaging no=0 and yes=1 and rounding to the nearest integer.)

Now suppose we each get a signal whose probability of accuracy is p[i], with p[i] unique to each individual but within the interval (0.5, 1).

Suppose we do not know the absolute value of our probabilities, but we can rank ourselves perfectly. Does it follow that we should let the individual with the highest probability of an accurate signal choose? Not at all. For a sufficiently large number of people, the probability that "everyone votes" gives an accurate answer is arbitrarily close to one. Perhaps the p[i] associated with the best among us is 0.95. We will have a 5% chance of choosing wrong if we delegate, and almost no chance of choosing wrong if we vote. If we have a large number of people with noisy but correct-on-average signals, we should still vote.

Now suppose p[i] is in the range (0, 1), and we can rank by p, but we do not know the absolute values. Then the optimal policy depends on the distribution of p. If the average signal is less than 0.5, we should definitely delegate to the most expert among us, although not necessarily to one person. If the right tail of our distribution is likely to be high, we may be better off letting a committee of experts vote than letting the most-likely-to-be-right individual choose, again because averaging reduces variance among answers with a good mean, and that may more than overcome the advantage of the person with the best individual probability.

Suppose p[i] is in the range (0.5, 1) but the number of individuals is small. Then, again, the best policy depends on the distribution of p[i] and the number of individuals, even if we can perfectly rank. If the population is large, voting is almost always best. If the population is small and the best of us are likely to have p sufficiently close to 1, delegation to experts is best.

So, the answer is, "it depends." Under some circumstances, delegation to experts is best. Under other circumstances, voting is best.

Note that imperfect rankability of p[i] almost always tilts towards voting. In practice, I think this is very important. I think people are not unbiased judges of their own rank, that it's plausible that people with the best judgements self-evaluate consistently low and those with the worst are systematically overconfident. That really kills a decision procedure based on self selection of judgment.

But again, even if accuracy of the signal is perfectly rankable, there are lots of circumstances in which voting is the right way to go. Delegation to the single best expert only makes sense where the right tail of the distribution of p[i] has significant mass near 1.

Of course, Min said first most of what I just said, only much more concretely and concisely!

Min and Steve's Wisdom of Crowds objection now sounds much more right to me. But both (I think) are assuming that the probabilities of error are independent, so tend to fall with large numbers of voters. Would that assumption make sense?

And, in general, wouldn't the weaker claim still be correct, that some fraction of the electorate (depending on the correlation between mistakes and the distribution of judgement) morally ought to abstain? What would the cutoff be?

Very interesting argument. It explains well why I did not vote at student elections in university and why I feel reluctant to vote at city council elections. All the candidates are equally unknown to me, and my vote feels arbitrary and therefore not moral.

On national elections, I have a broader view of democracy. I don't think it is just about making an optimal choice on who gets elected in order to make optimal decisions that maximises the country's comprehensive wealth and optimises the distribution of its wealth. Democracy is also about broad participation and responsiveness to the well-being of individuals and communities within the country. In Australia, participation in the democratic process is so important that voting is compulsory. I understand there is a modest penalty for not voting.

I am not sure what to make about the assumption that morality implies a capacity to be an unbiased estimator of our own judgment. Suppose my mental capacity is impaired so that I am unable to make an unbiased estimate of my judgment. Am I therefore not moral? Suppose "alpha males" overestimate their judgment, are alpha males therefore not moral? Maybe there is a link between morality and the capacity to make unbiased estimations. Or maybe I've misunderstood the argument. (Sorry!)

In any event, I would want immoral people to vote. Recognising that immoral people can and will vote, what should a moral voter do?

Kien: "Very interesting argument. It explains well why I did not vote at student elections in university and why I feel reluctant to vote at city council elections. All the candidates are equally unknown to me, and my vote feels arbitrary and therefore not moral."

That was what was at the back of my mind. In some votes, I feel "how the hell should I know?"

I expect if there is a large number of voters, Min and Steve would perhaps argue that the totally ignorant voters vote at random, and so probably cancel out by the Law of Large Numbers. But what if they all, unconsciously, vote for the same pretty face?

Even the knowledgeable voters will be swayed by a pretty face. But I would agree that random votes decrease the probability of the "right" candidate winning.

Steve: "I think people are not unbiased judges of their own rank, that it's plausible that people with the best judgements self-evaluate consistently low and those with the worst are systematically overconfident. That really kills a decision procedure based on self selection of judgment."

I think that's important. Yeats: "The best lack all conviction, while the worst Are full of passionate intensity."

Your outcome makes sense given the model, but obviously your definition of "morality" does not fit most voters. I don't think people vote because they think they think they want to give others a gift of what they believe to be the best possible outcome.

I think most people vote out of "civic duty." People get positive utility from simply showing up at the polling booth because they think partaking in the activity itself is "the right thing to do," regardless of outcome.

Hang on. Who actually believes that the Wisdom of Crowds argument applies? There is a very large number of voters in Canada. If voters' errors were independent, that number is large enough for WOC to get the right answer almost certainly. Does anyone believe that in all past elections, the party that won was the best party, given the information available at the time? Or do we think that all the other voters (except people like us) voted selfishly?

What if dynamics is added to the model? That is, what if people are able to change their vote some time later if they feel they made a mistake the first time round?

Nick, the argument that you described in this post is wrong, I think, for all of the reasons outlined in the comments. Morality is multi-dimensional - e.g. one party might support the moral belief that people have a right to die if they choose, another party might support the moral belief that we have a responsibility to future generations not to totally mess up the environment. It's not just about deciding whether or not a party's position is morally right -most have morally right positions on at least some issues - it's about deciding whether the parties have *important* morally right positions. Still, interesting and thought provoking. Great post.

David: you're probably right. Mike's post (that inspired this one), plus the comments there, are better on why people in fact vote. Mine is more of a "what if?".

DavidN: If you had to vote, but could change your vote after seeing how others voted, I think my argument says you would get unanimity. (People who believed they were worse judges than average, and who voted against the majority, would change their votes.). This is possibly one explanation for lawn signs and polling.

Frances: but maybe we recognise that our own judgments on the relative importance of moral issues might be wrong? We ought to!

Nick: "but maybe we recognise that our own judgments on the relative importance of moral issues might be wrong? We ought to!"

The question is: is the relative importance of moral issues a moral question (in which case it's a matter of judgement, and your judgement might be better than mine), or an empirical question (in which case it's a matter of knowledge, and the more knowledgeable person might not be the more moral person, or we can appeal to the wisdom of crowds in some respect )?

E.g. environmental issues become more important when we have the technological ability to totally destroy the environment, euthanasia becomes more important as the population ages, and more people start to suffer from long-term illnesses that reduce their quality of life.

RSJ, Aumann's Agreement Theorem requires perfect knowledge of everyone else's priors; in this case, that would mean perfect knowledge about everyone's preferences about swimming versus tax cuts. Nick didn't define what moral means, but if it means that every voter attempts to optimize the preferences of the entire population, rather than just himself, that would suffice.

Of course, that leads to Min's point: who needs an election, given these axioms?

Phil, I don't see it.

Auman's Agreement Theorem is about trying to agree on the likelihood of outcomes.

It's not a method to arrive at a decision.

I agree that you prefer tax cuts. You agree that I prefer swimming pools.

We both agree that we cannot have both swimming pools and tax cuts.

We are in perfect agreement about the world.

Nevertheless, we have to decide on what to do.

We would both agree to hold a vote.

Nick, I get it that this post is tongue in cheek, but I feel compelled to observe that the logical Bayesianism that you are leaning on here is far from the only school and possibly not the most influential or accepted. I think that de Finetti, for instance, would have regarded the axioms required by Aumann to be neither true nor false, but ill-posed, or meaningless, like Wittgenstein's "nonsense questions." Of course, de Finetti had many controversial opinions - most notably, his rejection of countable additivity (though he himself was the author of an important representation theorem in the infinite case.)

"some fraction of the electorate (depending on the correlation between mistakes and the distribution of judgement) morally ought to abstain"

So maybe it's already happening. In Canada and the US a sizable chunk of the electorate does abstain, mostly be cause they don't know/don't care and thus can't make an informed choice.

Steve Waldman: "Of course, Min said first most of what I just said, only much more concretely and concisely!"

Thank you for your kind words, Steve, but you are way ahead of me. I was going to do some generalizing this morning, but then I saw your excellent contribution. :)


Nick Rowe:"Min and Steve's Wisdom of Crowds objection now sounds much more right to me. But both (I think) are assuming that the probabilities of error are independent, so tend to fall with large numbers of voters. Would that assumption make sense?

"And, in general, wouldn't the weaker claim still be correct, that some fraction of the electorate (depending on the correlation between mistakes and the distribution of judgement) morally ought to abstain? What would the cutoff be?"

Oh, yes, the question of independence is very important. The pairing of non-votes in legislatures is one effect of dependence.

As for who morally should or should not vote, maybe only independents should vote. Political parties produce dependencies which do not have to do with the merits of the question to be voted on.

Here is a thought about the pre-vote stage.

In my example with three potential voters, suppose that B knows that A is more likely to be right than he is. Should B then defer to A, and vote the same way? The answer is plainly no, even though B is therefore more likely to right. The effect on the vote would be the same as if A cast the only vote. Independent judgement is very important. :)

But what if B went to consult with A? That would introduce a dependency, but I am not sure what it is, or what effect it would have. B may well change A's mind, but if that happens because of evidence and logic instead of charisma and persuasion, wouldn't that be to the good? And there is the possibility that B will change A's mind. Since A is more expert, it seems to me that that would be even more likely to be to the good. My sense is that in general the consultation would increase the probability of both being right, to the general good. :)

I think it comes down to whether a person can also be an unbiased judge of their independence. If there is a distribution of dependence (like Beta for stocks but with an assumed inefficient risk/return market) then you can imagine efficient frontiers of voters based on combinations of accuracy and dependence. If everyone was independent everyone should vote for reasons discussed above, plus the fact that you can really only hope for unbiased relative accuracy. Who is going to assess themselves as worse than a coin flip? And does dependence assessment create circularity problems given that your individual Beta will vary based on the ultimate voting population? Does it require that you know a lot about the distribution of others' dependence?

Surprised no mention of Jason Brennan's "Ethics of Voting".

Political scientist Andrew Gelman says there's no evidence voters are swayed by appearance:
http://www.stat.columbia.edu/~cook/movabletype/archives/2011/04/political_pundi.html

In case anyone's interested, Min and Steve's arguments (and Nick's to some extent) were made over 200 years ago by Condorcet - check out: http://en.wikipedia.org/wiki/Condorcet's_jury_theorem. Interesting thought experiment however.

Nick: "but maybe we recognise that our own judgments on the relative importance of moral issues might be wrong? We ought to!"

What do you mean "wrong?"  Moral propositions are not right or wrong; they logically derive from particular moral axioms, or not.  But *any* coherent moral proposition could be axiomatic if you want, or you could produce some other set of axioms that imply it.

I thought this was where you were coming from (or at least it's how I think Robin Hanson would approach it):  Normative (moral) propositions are in a practical sense undecidable because they simply reduce to a choice of axioms.  A Bayesian would weight all alternative axioms equally.  Therefore all rational beings agree.  

But even if I accept that argument (and I don't - for one you can't define the space of all moral axioms), then your argument immediately falls apart, because there is no reason to accept altruism as a superior moral principle.  Like any other principle, it surely follows from a mere subset of all possible moral axioms.  "Four legs better than two" is exactly equally deserving.

Your premise appears to be that there is one "right" and therefore moral choice. I would submit that each voter has their own set of morals, and the purpose of elections is to send someone with similar morals (and hopefully better judgement) to go and make the big choices based on our shared values.

There isn't so much a wrong choice, as a choice that's inconsistent with your own moral values. It's hard to argue that some other voter will be better suited to pick someone that's more consistent with my set of morals.

Also, when did WCI become a philosophy blog?

Voting is not about being right. Voting is about expressing your interests.

Also, the proper scope of analysis is not the individual voter but the institutional effects. What are the institutional effects of not voting?

We can see some of them. Voter suppression is well developed in the US. The effect is to clearly advantage the power of richer and better connected people.

We can also look back in history. The lowest voter turnouts that I am aware of in systems not clearly accepted as corrupt dictatorships is the Jim Crow South. Voter turnouts were in the 15% range in the early 50's in elections without a presidential vote. Which is cause and which is effect is an open question, but I would look long and hard at the democratic legitimacy of any low vote system.

Following on Min's thoughts: often, especially in small committees, the vote is a formality. Sometimes it never takes place at all. People discuss the issue, and reach a consensus. All the Aumann stuff gets worked out pre-vote. In larger committees, and countries, it's harder to do this. But maybe the vote itself is a form of discussion? The fact that (in civilised democratic societies) people generally respect the results of the vote might be simply because they are swayed by the Wisdom of Crowds. We each vote our priors, and the vote pools our information and tells us our rational posterior. I'm not explaining that very clearly.

K: "What do you mean "wrong?" Moral propositions are not right or wrong;..."

I've never believed that. I don't think anyone really does. We argue about what is morally right or wrong. We try to convince others. Sometimes we even succeed. None of that would make any sense if morality were just like personal tastes.

Neil: We do I think vote for people who share our values. But I think we also vote for people who share our beliefs about the world.

"Also, when did WCI become a philosophy blog?"

There's not a very clear dividing line between economics and philosophy. There have been times when I am not sure whether I'm reading a philosopher or an economist. (And I don't just mean the old guys, like Smith and Mill). I found my own transition from undergrad philosophy to graduate economics fairly seamless. Except for the math. (But then I have sat through a philosophy class where the board was also full of unintelligible symbols and theorems.) Phil Koop above is talking about de Finetti and Bayes. I learned about de Finetti in a philosophy course, and Bayes in an econometrics course. I wonder if Phil learned about them in courses with the prefix PHIL, ECON, STAT, or MATH? Or even FIN? There's a lot of overlap.

Jim: Do people only vote their own interests? Politicians do spend a lot of time trying to convince voters what is right, as well as what is in their interests. We all do. They presumably wouldn't do that if they knew that people only voted their interests.

Sometimes I think a low turnout is a good sign. It might mean most people think that whichever candidate wins will give tolerably good government. Obviously there are other interpretations. But countries where people are very passionate about politics are usually screwed up countries. Whether as cause or effect.

All: this is certainly one case where I am not going to stick to my guns and defend my original thesis. (I'm very glad I put in that bit about "I am almost certainly muddled somewhere."). But I'm still glad I posted it. The discussion has been very good. I'm not responding to all comments; simply because I don't have any useful responses to many.

Nick: "But maybe the vote itself is a form of discussion?" There is a whole school of thought out there that sees politics as a process - the fact that we all have a say is a good thing in itself. We talk about things during the vote.

On consensus: the always awesome David Mitchell on consensus here.

"K: "What do you mean "wrong?" Moral propositions are not right or wrong;..."

I've never believed that. I don't think anyone really does. We argue about what is morally right or wrong. We try to convince others. Sometimes we even succeed. None of that would make any sense if morality were just like personal tastes."

Hmm, we also argue about tastes and try to convince others. And religion. Is there a *right* religion? Our own tastes also change. People as a whole change.

But politics is not about morality, it's about preferences.

The point is, regardless of whether or not there is a "right" preference for everyone to have, we've decided that that question is outside the scope of the power allocation process, just as the question of whether there is a "right" utility is outside the scope of an economic model. We assume it is an exogenous variable.

But that still leaves open the door for campaigns, leaflets, soap-boxes and other efforts to try to change people's minds,

Nevertheless we still hold the actual vote because we respect the dignity of the individual above our desire to be "right", or to arrive at the right policy. This is itself a value statement, which says that decisions arrived at illegitimately are themselves illegitimate, as the point of the exercise is to maximize people's happiness, not fulfill some objective goal.

Jim Rootham: "The lowest voter turnouts that I am aware of in systems not clearly accepted as corrupt dictatorships is the Jim Crow South. Voter turnouts were in the 15% range in the early 50's in elections without a presidential vote. Which is cause and which is effect is an open question, but I would look long and hard at the democratic legitimacy of any low vote system."

As it turns out, I grew up in the Jim Crow South. It was solidly Democratic. The action was in the primaries, as most candidates ran unopposed in the general election. I could not vote, but I would not be surprised if the turnout for the primaries was much larger. :)

Nick Rowe: "But maybe the vote itself is a form of discussion?"

Great minds think alike. :)

Nick Rowe: "The fact that (in civilised democratic societies) people generally respect the results of the vote might be simply because they are swayed by the Wisdom of Crowds."

Having grown up in the Jim Crow South, I am rather skeptical of the Wisdom of Crowds. ;)

Nick: "this is certainly one case where I am not going to stick to my guns and defend my original thesis."

Never thought you meant it seriously in the first place. I just took as a challenge to a philosophical debate. Not quite done yet either...

I agree almost completely with everything RSJ says. But lots of people's preferences have a lot to do with the morality of other peoples behaviour or the morality of government programs. And morality is a special preference since people will not always accept to subjugate their moral principles to a system of government. Take abortion, capital punishment, same-sex marriage, pot smoking (today) or alcohol consumption (80 years ago). Some may judge these issues based on a social welfare function and those people may be able to settle their differences based on a rational exchange of ideas and information, and mutual consideration of each person's relative advantages in terms of experience and relevant forms of intelligence: truth-seeking Bayesians *never* give intrinsically greater weight to their own opinions. But if it turns out that those opinions reduce to conflicting axioms, then, in order not to have to "agree to disagree," those Bayesians will agree to weight those axioms equally.

But most people have some opinions that are not subject to rational argumentation because they reduce to conflicting axiomatic choices on which they are not willing to compromise. We do not agree on the meaning of "thou shalt not kill", in part because we do not agree on the definition of person. Does "person" include the unborn, infidel, murderous, primate, or cow? Cockroach? Is it worse to kill a fetus, or a chimpanzee? How about a profoundly mentally handicapped person or a chimpanzee? Don't forget, there's a continuum of mental states between "profoundly mentally handicapped" and "vegetative". Peter Singer says the chimp can be worth more. Anything else is paramount to "two legs better than four" - also a common moral axiom. Any absolute answer to these questions will depend on selection of some particular set of moral axioms. People can, *and do*, select differently.

And in economics, at its core, are disagreements between those (Austrians, libertarians, many right wingers) who believe in little more than Pareto optimality with its roots in deontological ethics (and ultimately in the categorical imperative - also an axiom), and those (liberals, left wingers) whose beliefs often lean more towards purely consequentialist utilitarianism. But deontological and utilitarian ethics are not equivalent, nor can one be derived from the other. At the core they have different axioms (i.e. moral preferences) that cannot be logically reconciled.

Yet others, see morality, like consciousness, as little more than evolutionary adaptation in a totally mechanistic world. So they have little reason to hope for the existence of any satisfactory and logically consistent system of moral reasoning. But perhaps, Nick, you are religious (or maybe you feel that absolutism is a necessary antidote to relativism) and therefore you believe that there exists some set of absolutely "right" axioms. But I don't see how these absolute moral principles would be obtained, as you suggest, by a truth-seeking Bayesian. Such a person could, at best, hope to determine the set of all possible sets of moral axioms and weight them appropriately. Our current system of government attempts to do that, however crudely, via voting. Robin Hanson proposes Futarchy, a system of government in which we "vote on values but bet on beliefs". I.e. he specifically distinguishes between decidable propositions ("beliefs") which he proposes to settle via a market mechanism, and undecidable ones, i.e. preferences ("values") which are settled via voting.

Nick,
I've made this comment before on similar issues - stop thinking that the aim of voting is to produce the best decision. The aim is to give the decision legitimicy. Therefore everybody should vote - responsibly and consciencously (as if they carried all the responsibility for the decision).

Of course the way to vote conscienciously and responsibly might be to see what the best expert is saying and follow his advice.

P.S. Does anybody else have problems posting here - some of my keystrokes are being lost - the focus seems to keep changing.

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