Asher + The possibility of social choice

Asher

Imagine a human called Asher.

Asher is bad (though not wholly wicked), and known to be bad. Asher is unloved, and their memory is damned- whatever Asher does, they will always be known to have been bad as long as their memory persists. Asher holds no delusions about being, or becoming, a good person.

Asher is given a choice by circumstance- they can die, a lonely and unknown death trying to do the right thing- say, trying to save some innocents- or they can keep on living. Asher has no hope that this will redeem them and so make them, on the whole a good person and no hope that this will redeem their memory- no one will know. Moreover, Asher has no special identification with those they will die to save, beyond their shared humanity. They are not Asher’s children, or friends, and they will in no way continue Asher’s projects.

All other things being equal, Asher would prefer to live than die, though their life is miserable. Nonetheless, compelled by the need to do good, and perhaps the need to salvage what they can of their life, Asher makes that lonely sacrifice.

Asher’s sacrifice seems to me, in at least one sense, the purest act of good imaginable.

I am curious about this character. I know of many characters in fiction that died heroic deaths and there are many characters in fiction who die to redeem themselves and their name, but I can’t think of a story like Asher’s.

It’s interesting and a little sad to reflect somewhere and somewhen, there probably was an Asher.

The possibility of social choice

We all know of Arrow’s impossibility theorem:

In short, the theorem states that no rank-order electoral system can be designed that always satisfies these three "fairness" criteria:

• If every voter prefers alternative X over alternative Y, then the group prefers X over Y.

• If every voter's preference between X and Y remains unchanged, then the group's preference between X and Y will also remain unchanged (even if voters' preferences between other pairs like X and Z, Y and Z, or Z and W change).

• There is no "dictator": no single voter possesses the power to always determine the group's preference.

But I suspect, in very informal terms, if the following is true:

• There is a finite group of voters and a finite list of proposals. Each voter has an preference ordering over the proposals.

• A proposal can only pass if a majority vote for it. Voting is on a proposal by proposal basis.

• A new compound proposal can be formed by making a lottery, e.g. if P & Q are proposals, (a 70% chance of P and a 30% chance of Q) is itself a proposal. The lotteries can have any number of possible outcomes (e.g. a lottery over P, Q or R would also be acceptable). Each voter has a preference ordering over all possible lotteries. [This guarantees cardinal utilities].

• Voting proceeds by a series of rounds in which a proposal is made by a voter, and then knocked back or accepted.

• Voters want the deliberation to be done as soon as possible. Each new round imposes a utility cost - due to the costs of being their, or due to the costs of not having come to a decision.

• There is at least one proposal, P such that a majority would prefer it to deliberations being dragged out past some finite length L. [If nothing else, P can be the decision to leave things at the status quo]

• Voters all know each other’s preferences and preferences over lotteries and are rational.

Then the voters will come to a majority decision. This has some key differences from Arrow’s case that make it more tractable- pressure to agree, plus cardinal preferences.

The intuition more generally is that if a decision has to be made and deliberations impose costs that, for a majority, can eventually grow to be larger than at least one of the proposals on the table, a majority decision will be made in some finite time. I’m pretty sure the relevant truths have been shown for game theory generally, what I’m not so sure people have noticed is that, practically speaking, this shows the possibility of democratic social choice.

The final condition re: knowledge is very strong, but I suspect that, in practice, settling on a decision - even if it’s the decision not to decide - will almost always happen through bargaining even if both players don’t start with this knowledge. If the players don’t know each other’s true utilities it becomes a complex bargaining game, yes, but one that seems like it should be soluble in a finite amount of time.

I think it works with a variety of modifications- e.g. requiring supermajorities, requiring unanimity.

But this result- already I think shown by others- seems to me, in practice, much more important that Arrow’s theorem.

Edit:

I realize I’ve done that thing I so often do, float an idea and insufficiently justify it. Why think that, in practice, that if this result is true it is much more important than Arrow’s theorem? If we can establish that: if the incentives to agree are enough, at least a majority will eventually agree that is all that is needed to make real life social choice viable, because in the real world there are huge incentives to come to an agreement. That gives much more hope to me than Arrow’s theorem takes away. There’s no need to impose these pressures on people- the world, the costs of deliberation, and the benefits of agreement (especially timely agreement!) force majority formation.

To put it in even simpler terms, if it’s in a majority’s interests to pass a motion, they will. If there are multiple motions that would improve their utility, they will negotiate over which, or make a compound proposal using lotteries, and pass one. This seems both tractable and not inherently ethically disturbing (there’s no dictator etc.). I’m pretty sure all this is mathematically trivial. But this meets the most practically significant sense of social choice. That’s it. There’s little more to say. Once we have cardinality, time, and negotiation we have all the goodies we need.