[Election-Methods] Challenge: Elect the compromise when there're only 2 factions

[Jobst Heitzig]

Dear Abd ul-Rahman,

> I am most concerned about majority *consent.* Jobst is ignoring the 
> fact that I'm suggesting majority *consent* for decisions; 

What exactly is "majority consent"? In my understanding "consent" means 
*all* voters share some opinion...

> what do you call it when a minority imposes its will on a majority?

It is not democratic whenever some group can impose its will on the 
others (in the sense of making their preferred outcome certain). No 
matter whether that group is a majority or a minority. From this it 
follows that a method which is always deterministic cannot possibly be 
democratic.

> Question: if the majority explicitly consents to this for a specific 
> election, does the election method satisfy the Majority Criterion?

If the system would have allowed the majority to decide otherwise, the 
*system* is majoritarian.

>> > I'm not sure at all what a "just share of power" is.
>>
>> Me neither. But no power at all is definitely not a just share of power.
>> By posting on this topic I hope a discussion on this will eventually
>> begin.
> What I pointed out here was that the ratings given did not contain 
> sufficient information to determine justice. 

Yes it does. I gave a reasoning why I consider C the more just solution 
because everyone prefers it to the "democratic benchmark".

> Again, without defining justice, but relying upon common understanding 
> of it, we can easily construct scenarios that fully explain the 
> ratings as sincere, but which have quite different implications 
> regarding justice. In the challenge election, to repeat, we have
>
> 55: A 100, B 0,   C 80
> 45: A 0,   B 100, C 80
>
> It was assumed that the ratings were "sincere," though that was not 
> defined.

I gave at least two interpretations of this, so it was defined. I prefer 
the "preferences over lotteries" interpretation.

> Now, it's obvious that C is what we would ordinarily understand as the 
> best winner. But a majority will disagree, and thus the challenge. I 
> don't recall the exact wording, but is there a method which, if 
> adopted, would cause C to win, even if the A and B voters are selfish, 
> and we might assume, the A voters know that they are in the majority?
>
> The answer given was Borda with equal ranking prohibited. Now, when I 
> first read this, I did not properly understand it. I should repeat 
> what I did before, only correctly.
>
> Let me be explicit about how this could elect C. I will modify the way 
> Borda count from how it is usually stated to make it equivalent to a 
> Range 2 election (CR 3).
>
> Sincere votes.
>
> 55: A>C>B
> 45: B>C>A
>
> Counts: A, B, C
>
> 55: 2 0 1
> 45: 0 2 1
>
> totals:
>
> A 110, B 90, C 100. This does not elect C. However the B voters, if 
> they understand the situation, can vote
>
> 45: C>B>A
>
> or counts A, B, C:
> 45: 0 1 2
>
> totals:
> A 110, B 45, C 145. C wins, so it appears a quite desirable strategy 
> for the B voters, as we would understand the sincere ratings.
>
> Is there a counter-strategy? What if the A voters reverse their second 
> and third preferences?
>
> 55: 2 1 0
>
> With the strategic votes from the other side the totals are
>
> A 110, B 100, C 90; they defeat the compromise attempted by the B 
> voters. However, the gain is relatively small, it would seem (but 
> there is an assumption that a gain of 20 in rating is "small." Not 
> necessarily.)
>
> and with the original sincere Borda votes from the B voters, this 
> counterstrategy would give us
>
> totals
> A 110, B 135, C 90.
>
> So, somewhat off the topic, but interesting nevertheless, the B 
> voters, being not only selfish, but clever, mount a secret campaign to 
> get all the B voters to vote the strategy. However, they also arrange 
> to leak this information to the A voters, and, *supersecretly*, they 
> are not going to do that, they are going to vote sincerely. If the A 
> voters fall for it and vote strategically, to defeat the nefarious 
> stratagem of the B voters, and the B voters then simply vote 
> sincerely, B prevails, which is a disaster for the A voters and a 
> total victory for the B voters.
>
> The A voters are *probably* better off simply voting sincerely. And 
> that was Jobst's point. 

I don't think that was my point. In order to get a stable situation, 
i.e. a group strategy equilibrium, all voters should order reverse to 
make sure the other faction cannot reverse the outcome to their 
advantage. So the A voters are better off voting C>A>B. For this reason, 
I consider Borda a possible but not a good solution to the problem.

Juho's suggestion to use weights like 1.4, 1, and 0 improves this since 
with them C is already elected with sincere ballots.

> Explicitly, Jobst stated that the ratings given were not utilities, 
> and that he doesn't believe in utilities as having any meaning.

Again, this is not true. I only stated that I don't believe in 
*measurable* utilities or, most importantly, even in *commensurable * 
ones. That does not mean I regard the term "utility" as meaningless. 
When someone prefers some A to some B, I think we can interpret this as 
A having "more" utility for her than B. But this "more" need not be 
representable by real numbers.

Yours, Jobst