[EM] Heitzig consensus and brinkmanship

Kevin Venzke stepjak at yahoo.fr
Sun Aug 2 12:46:48 PDT 2020

 Hi Kristofer,
    Le mercredi 29 juillet 2020 à 12:45:02 UTC−5, Kristofer Munsterhjelm <km_elmet at t-online.de> a écrit :  
 On 16/07/2020 02.02, Kevin Venzke wrote:
>>> 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
Absolutely it shows that they aren't exactly the same. I understand what you are saying,so it becomes maybe a terminology issue that may not be of interest. But for me there arethree concepts here:1. the minmax objective, as you say.
2. enacting the median voter's position, which is how I would interpret "improve the conditionof the median voter," though I understand this is not really the concept you are using inthe pizza example.3. the result you might expect from a majoritarian or strategic Range election, meaningmerely that the median voter will be included in the victorious majority.
You can see the potential for difference between 2 and 3 by putting "heavy pepperoni" and "light pepperoni" in your example and arranging it on a spectrum, placing a smallnumber of "light pepperoni" supporters at the median. It becomes unclear whether "light"will win under a majoritarian method. It's only clear that some pepperoni option will win.
What I mean by 1 and 2 being "naively the same" is that if you generate scenarios randomly in issue space, they are probably the same. Or at least similar enough thatif it's easier to address the problem by focusing on 2 and not 1, maybe that's worth it.
The pizza scenario highlights the situation where 1 differs from 2 and 3. But I think it'smore common that 3 is the outlier. That disturbs me because it seems that 2 should beachievable without even deviating from majoritarian principles.

>> 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 of 
>> 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.
Yes, you're right. There would at least need to be a clear cost to the participants for forfeiture of office to be an effective tool.
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