[EM] Does IRV elect "majority winners?"

[Kristofer Munsterhjelm]

Dave Ketchum wrote:
> On Thu, 08 Jan 2009 11:51:36 +0100 Kristofer Munsterhjelm wrote:

>> The point is that it's an advantage to the voters to express their 
>> thoughts in this manner. It's kind of like if Condorcet weighted votes 
>> by 1 / (number of ranks specified) so that it made sense to bullet-vote.
> 
> It is a convenience, but no advantage as to power of their votes.

It's a mere convenience to Condorcet voters. To Range voters, voting 
Approval style (certain edge cases notwithstanding) is a definite power 
advantage.

Say that the election is so far A: 99.8, B: 99.4, C: 37.4, and your 
sincere preference is A: 0.4, B: 0.7, C: 0.2. You'd prefer B to win, so 
you say A: 0, B: 1, C: 0.

>>>>> I am still trying to promote series thought as to need for a 
>>>>> majority for other than Plurality or Approval.
>>>>
>>>>
>>>>
>>>> A worst-case point of view might be to consider the groups maximally 
>>>> different. That is, nobody who voted A > B also voted A > C. From 
>>>> that point of view, and a strict interpretation of "majority", one 
>>>> would have to have the weakest victory be one of a majority - that 
>>>> is, for the candidate X so that the magnitude of the win of A 
>>>> against X is least, A must beat X by a majority.
>>>
>>>
>>> Let me offer bullet voting in Condorcet:
>>>      32 A
>>>      33 B
>>>      34 C
>>>
>>> C wins because, with 99 voters, C's 34 makes it CW.
>>
>>
>> That's true. I was talking about Condorcet majorities, though, and 
>> none of those would have such a majority.
>>
>> In general, if you have a voting method and everybody bullet-votes, 
>> then you pretty much have to reduce to Plurality, since there's no 
>> other information available.
> 
> I do not HAVE to reduce Condorcet to Plurality here, for the voters have 
> provided valid Condorcet votes.
> 
> However, if bullet voting is common enough in Condorcet elections, it 
> could make sense to count as if Plurality until ranking is seen, and 
> then adjust and continue counting by Condorcet rules.

What I mean is that if you have some method, and the input is only 
bullet-vote ballots, the method pretty much has to act as Plurality 
would in that case. That is, the method "reduces" to Plurality in the 
case of everybody bullet-voting.

Condorcet reduces to Plurality since if all votes are bullet votes, 
they're effectively of the form

A > B = C = D
B > A = C = D
C > A = B = D

meaning that a vote for whoever was bullet-voted is a vote for that 
candidate in preference to all other candidates, hence a candidate that 
would win Plurality is a CW if everybody bullet-votes.