[EM] The company Approval election of committee-members

[MIKE OSSIPOFF]

I agree that your first proposal is the best: One Approval balloting for the 
manager position. And a 2nd Approval election to elect the rest of the 
committee. In the 2nd balloting, the 8 top votegetters win.

And, in those Approval ballotings, people should be able to mark (or write) 
the names of as many candidates as they want to.

Ideally it might be better to hold 2 ballotings for each election, but that 
would be a complication, and would be asking people to vote twice as many 
times. Usually keeping it as simple as possible and minimizing how many 
times people are asked to vote are the important considerations. So I 
suggest doing it exactly as you said in your first proposal.

About the strategy recommendation, if it's 0-info, the strategy of voting 
for everyone who is above the mean is the best thing to recommend for the 
single-winner election of the manager committee member.

For the 8-winner election of the other committtee-members, I don't think any 
of us have studied several-winner strategy. But it seems to me that the same 
strategy, voting for everyone who is above the mean, is still the best one, 
or at least a very good one, even for 8 winners.

That's because: Say, for simplification, there are several 8-member slates 
running. Say each voter has a favorite slate, and has merit-ratings for the 
slates. It seems a reasonable simplifiation to treat each slate as a 
candidate in a single-winner election.

As a simplification, say that all tlhe members of a particular slate are 
equally good. So if you vote for every candidate who is above-mean for you, 
then you're helping every slate that is above mean for you.

A person could actually vote in that way, voting for all the members of each 
slate that s/he considers above-mean. But, with the simpliflying assumptions 
I've suggested, voting for all the above-mean candidates has the same 
effect.

Because voting for the above-mean candidates gives the same results as 
voting by slate, with those reasonable simplifying assumptions, I claim that 
voting for the above-mean candidates is a good strategy even when there are 
going to be 8 winners.

It may well be that someone else will suggest a strategy especially written 
for Approval when there are several winners. In the meantime, however, I 
suggest just voting for every above-mean candidate.

It was also pointed out some time ago that, when there are only a few 
voters, the above-mean strategy isn't strictly optimal. But my answer to 
that was, and is, that any suboptimality resulting from using above-mean 
strategy when there are only a few voters is swamped by the suboptimality 
resulting from errors in estimating how high the various candidates should 
be rated.

If the election isn't 0-info, then a good strategy to suggest would be the 
one that Forest proposed some time ago: the better-than-expectation 
strategy: Vote for each candidate who is so good that you'd rather have 
him/her in office than hold the election, if that were up to you. That's 
been shown to maximize the voter's expectation, with a few reasonable 
approximations. Under 0-info conditions, the better-than-expectation 
strategy becomes the same as the above-mean strategy, since the candidates' 
mean merit is the expected value of the election when there's 0-info.

If the election isn't 0-info, then the errors in perceptions about how good 
the result is likely to be is even less dependable than your estimate of who 
is above mean, because it includes uncertainty about what's going to happen. 
So it's all the more reasonable to say that, due to  these 
estimate-uncertainties, the suboptimality of using many-voters strategy in a 
few-voters
election doesn't cause suboptimality that matters in comparison to the 
suboptimality resulting from those uncertain estimates.

You said that the voters wouldn't want to hear about numerical utilities and 
probabilities, and so the abovementioned strategies are the ones to 
recommend.

Mike Ossipoff

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