[EM] Does IRV elect "majority winners?"

Kristofer Munsterhjelm km-elmet at broadpark.no
Wed Jan 7 02:15:45 PST 2009

Dave Ketchum wrote:
> Condorcet certainly costs more for the system than Plurality.  Costs 
> bullet-voters nothing - provides a service to whichever voters like to 
> do more than bullet vote.
>      Actually can be a service to candidates.  Clinton and Obama had to 
> try to kill their competitor's campaign for the Democrat nomination they 
> could not share.  A similar race in Condorcet would let them both get 
> nominated and have a more civilized fight as to which should be ranked 
> higher than the other on the ballot.

If people tend to bullet-vote, it may be the case that elections in 
general suffer from vote-splitting - simply because if C splits into C1 
and C2, people either bullet-vote C1 or C2.

On the other hand, the mayor election data that was given on this list 
earlier seems to show that people don't bullet-vote as much as one would 
expect (even though one should be careful in deriving conclusions from 
sample sizes of one).

> Bucklin deserves more thought as a competitor to Condorcet.

Bucklin doesn't do that well, Yee-wise. It's simple, however; I'll grant 
that. As far as criteria go, it fails independence of clones, is not 
reversal symmetric, and can elect a Condorcet loser (according to WP).

> How do you count equal ranking in IRV?  If I vote X>A=B>Y, A and B 
> become visible to the counters at the same time - what does this do to 
> deciding what candidate is next to mark lost?

I would assume that if one does A = B > Y and A is eliminated, then the 
ballot becomes B > Y next - "the ballots are transformed as if the 
candidate in question never ran". The difference from A > B > Y or B > A 
 > Y would be that both would be counted the first time around, either 
with a full point to each ("whole") or half ("fractional").

> Approval, Plurality and IRV are distractions from need to pick a live 
> destination.  I see need to compare, more carefully, Condorcet vs Range 
> vs Bucklin.

Range reduces to Approval if enough people use strategy. I think that 
any version of cardinal ratings should either be DSV or have some sort 
of Condorcet analysis (like CWP does, or perhaps not that far). Those 
are my opinions, though, and others (like Abd) may disagree.

>>> The CW has been compared with EACH other candidate, and found better 
>>> liked in every case.  However this does not guarantee a majority, 
>>> since voters are not each required to rank all candidates.
>> That's right. And, in fact, it could only be a small minority who so 
>> voted, i.e., that the winner was "better liked." Majority requirements 
>> *require* that the electorate actually consider and accept or reject a 
>> winner.
> A "small minority" cannot win in Condorcet, except for the tortured case 
> of a zillion candidates with at most a small minority voting for any one.
> 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.

This encompasses the standard majority setting where a majority votes A 
 > [everybody else]. It's not equal to it, as one may see from this example:

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

B has a majority against C, D, and A.

It's also a worst-case point of view because it errs "safe" in the case 
of truncation - truncation so that A is not ranked on the ballot means 
that no victory for A above some other candidate will be counted for 
that ballot.

>>> BTW - cost of ballot support for complete ranking can tempt limits on 
>>> Condorcet ranking.  How bad should we complain if offered 3 as in RCV?
> Three seems like a good minimum, with cost vs voter desires controlling 
> whether more get implemented.

I don't know much about the cost of optical scanning machines, but 
presumably getting one with 8 or 10 sensors shouldn't be that more 
expensive than one with 3. They wouldn't have to be specialized, either, 
since optical scanning is used for other things than counting ballots.

The ideal solution as far as granularity is concerned would be to have a 
machine that does OCR, and where voters just write a number in a box 
next to the candidate (1 for first place, 20 for twentieth). That would 
be quite a bit more expensive, though, and would also need some sort of 
fallback... or just manual counting.

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