[EM] Heitzig consensus ...
fsimmons at pcc.edu
Thu Jul 30 18:09:25 PDT 2020
> In general it is easier to find a lottery that is unanimously preferred
> over the default lottery than to find a deterministic alternative that is
> unanimously preferred over the default lottery.
> 1. Re: Heitzig consensus and brinkmanship (Kristofer Munsterhjelm
> Message: 1
> Date: Wed, 29 Jul 2020 19:44:59 +0200
> From: Kristofer Munsterhjelm <km_elmet at t-online.de>
> To: Kevin Venzke <stepjak at yahoo.fr>, EM
> <election-methods at lists.electorama.com>
> Subject: Re: [EM] Heitzig consensus and brinkmanship
> Message-ID: <d303eb7a-8b08-5748-33ae-62e586c7cfaf at t-online.de>
> Content-Type: text/plain; charset=utf-8
> On 16/07/2020 02.02, Kevin Venzke wrote:
> > Hi Kristofer,
> > Le mardi 14 juillet 2020 ? 18:40:19 UTC?5, Kristofer Munsterhjelm
> > <km_elmet at t-online.de> a ?crit :
> >> I was thinking about the possibility of using the mechanism to direct a
> >> government or organization to act in a minmax manner: one that intend to
> >> make the worst off best off, rather than improve the condition of the
> >> median voter.
> > Just to interject quickly. To my mind these two things are (naively)
> > the same, and if results matched the preference of the median voter
> > you would have a good thing. What I expect instead, with two factions
> > fighting over who can capture a majority, is that the factions don't
> > propose (or don't enact) the median position. They want the vote of
> > that position, and those voters can come to the victory party, but
> > they won't be in control.
> Doesn't the pizza election show that these are not the same? Suppose the
> utilities are:
> 7 voters: Pepperoni 9, Mushroom 8
> 3 voters: Pepperoni 0, Mushroom 9
> The median voter prefers pepperoni. But a minmax outcome is the one that
> leaves the worst-off voter best off, and that's mushroom. In this case,
> the Heitzig consensus fails to deliver minmax, because the 70%
> supermajority prefers a random ballot to mushroom. But if it's
> two-sided, say:
> 6 voters: Pepperoni 9, Mushroom 8, Anchovies 0
> 2 voters: Anchovies 9, Mushroom 8, Pepperoni 0
> 2 voters: Anchovies 0, Mushroom 9, Pepperoni 0
> then the outcome of a random ballot is 0.6 * Pepperoni + 0.2 * Anchovies
> + 0.2 * Mushroom. The expected score is thus:
> To the group of 6 pepperoni voters: 7.0
> To the group of 2 anchovy voters: 3.4
> To the group of 2 mushroom voters: 1.8
> and everybody prefers mushroom to this, so it's in everybody's interest
> to choose mushroom as the consensus. Hence the minmax option wins, but
> in a majoritarian election method or a strategic Range election,
> Pepperoni wins.
> >> From what I remember, Jobst and Forest were originally
> >> trying to find a method to avoid a majority dictatorship, so my idea is
> >> in a way to consistently take that to its logical conclusion. If the
> >> state or the organization must pay attention to every voter, or to a
> >> supermajority of them, then it can't afford to leave some of them
> > badly off.
> >> But if it's to be used as a part of normal operating procedure, then it
> >> has to resist strategy to some degree, and it can't take the whole
> >> organization or state down with it at the first sign of trouble. So if
> >> the brinkmanship scenario is a problem, then either the mechanism has to
> >> be augmented to stop it being a problem, or the assembly has to somehow
> >> be able to keep the peace enough that politics will never become that
> >> contentious to begin with.
> > It seems like a tall order...
> Yes. I don't know of any other mechanisms that come as close as it does
> to implementing minmax, so it would be really nice if it could be made
> to work.
> >> Yes, that is a possibility - that a way out is to make the consensus
> >> option at least as good on expectation as the roll of the dice,
> >> discounted by whatever risk aversion exists.
> >> That's an important point, I think. The consensus option doesn't have to
> >> be extremely good. For it to be chosen, it just has to be preferred to
> >> rolling the dice by everyone. If it's barely better, that's still good
> >> enough to make it pass.
> > I think that may be true (if we rule out, as I say, a value to being
> > perceived as unwilling to compromise), but I wonder how often such a
> > consensus option could be expected to exist? I picture the math of it
> > very simply but it seems like it should be nearly a wash.
> > When you say "to make the consensus option at least as good" do you
> > envision some kind of mechanism that could actually improve what the
> > consensus option is? Or maybe, easier to imagine: a rule that imposes?
> > some kind of universal penalty if consensus isn't achieved. A forfeiture
> > office seems like the most obvious.
> I was thinking that the random ballot outcome can be quite bad. E.g. the
> expected scores in the two-sided pizza election:
> 6 pepperoni voters: 7.0
> 2 anchovy voters: 3.4
> 2 mushroom voters: 1.8
> If someone blinks (e.g. an anchovy voter mistakenly doesn't set mushroom
> as the consensus option), then the outcome is not particularly good for
> society as a whole. All we *really* need is the expectation of the
> lottery to be less than the consensus option, while resisting strategy.
> So in some ideal world, the expected value for the fair lottery would be
> something along the lines of
> 6 pepperoni voters: 8 - epsilon
> 2 anchovy voters: 8 - epsilon
> 2 mushroom voters: 9 - epsilon
> and even for very small epsilon, it would still be preferable to choose
> the mushroom consensus option. But how to implement such a lottery, much
> less in a strategy-resistant manner, I have no idea.
> In a way, it's like the concept of MAD: if you give every voter his
> personal doomsday button to push if he doesn't get a satisfactory
> outcome, then minmax will happen if it's at all achievable. However, the
> outcome should consensus be impossible is truly horrible. The better the
> system can be in the "no consensus" case while leaving consensus
> preferable, the better the method is.
> The other side of that coin is what I said in the earlier post: if the
> consensus option is always at least as good as a random ballot, then
> it'll always be chosen. So making the structure around the mechanism
> conducive to finding a consensus would also help.
> We'd have to be careful that the alternative to consensus isn't biased,
> though. "Forfeiting one's office" might well be, just like "status quo
> prevails" is.
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