[EM] Does IRV elect "majority winners?"

Abd ul-Rahman Lomax abd at lomaxdesign.com
Sun Jan 4 21:19:29 PST 2009

At 10:28 PM 1/4/2009, Dave Ketchum wrote:
>On Sun, 04 Jan 2009 16:16:14 -0500 Abd ul-Rahman Lomax wrote:
>>Perhaps. Perhaps not. That can be a *lot* of preparation, and 
>>people are busy, many don't already, find time for voting. Bullet 
>>voting is simple, it can be relatively easy to know who your favorite is.
>Agreed that bullet voting is often appropriate.
>Only occasional elections provide reason for some voters to do more ranking.

And only certain voters. It's relatively uncommon that there are more 
than two frontrunners, and most voters know who they are. Under those 
circumstances, the only strong reason not to bullet vote is if you 
prefer someone other than a frontrunner, and care to express it. The 
argument for Plurality would be that the system shouldn't be 
encouraging "useless candidates" to run at all! That is, since 
vote-for-one usually works, and the only reason it doesn't work 
(usually, and even this is fairly unusual) is that some silly voters 
will throw away their vote on a candidate who can't win, why should 
we respect the unexpressed wishes of those voters? After all, they 
had their chance! We don't run elections as a popularity contest, 
i.e., so minor party candidates can brag about how many votes they got....

*My* point here is that there are some reasons to prefer plurality, 
we often neglect them completely. Whatever system we try to 
implement, it's not likely to be stable if it is more work than it's 
worth. If all the system does is to, nearly always, confirm Plurality 
results -- and this is the case with IRV in nonpartisan elections -- 
it is a *huge* waste.

>Even if runoffs are possible/expected, it is wise to vote carefully 
>in the primary to minimize possibility of bad choices getting to the runoff.
>>And when it isn't easy to know, having trouble deciding between 
>>two, Open Voting (Approval) allows a simple option: vote for both!
>What is important is that Condorcet, unlike Approval, permits voting 
>for both Good and Soso, while indicating that Good is preferred.

Right. However, with American Preferential Voting (Bucklin), you 
*can* indicate your preferences. My point is only that equal ranking, 
if allowed, can be, actually, more expressive.

Looking over the ballots from Burlington, as I just did, I'm struck 
by how many voters do seem to imagine that their votes will be 
counted! Overvotes are more common than I'd expect if they were mere 
slips. It is very easy for me to imagine that voters think that if 
they vote for more than one candidate in one of the ranks, why, the 
votes will be counted, they are merely saying that, for first 
preference, they prefer either the Progressive or the Democrat, or 
some other combination. The fact is that if such votes were counted, 
they'd make sense, even in IRV. (Allowing equal ranking turns IRV 
into a much better system than without it.)

Those concerned about Later-No-Harm can simply avoid equal ranking!

>>If any Condorcet method is used, it should allow equal ranking, 
>>because this *allows* more sincere voting, in fact.
>AGREED that equal ranking should be permitted.

Permitting it with Plurality turns Plurality into a far better 
system, with no cost. Bucklin is very much like Open Voting (i.e., 
plurality with equal ranking allowed, i.e., Approval) except that it 
is possible for the voter to rank so that votes are counted in 
rounds. The original Bucklin only allowed multiple votes in the third 
rank, but I don't see any reason to *prohibit it* -- i.e., discard 
ballots that equal rank -- in the first two ranks.

It makes one less reason to discard and not count a vote....

In the Burlington election, there were 77 "blank" ballots, if we can 
believe the images. I suspect that, in fact, some of these weren't 
blank, but that they had no vote in the first rank. Another technical 
reason to discard a ballot. A voter thinks, "I really don't like any 
of these guys much, so I'll just leave the first preference blank -- 
not realizing that, probably, by the rules, the ballot won't be 
counted at all." IRV is *complicated.*

On a Bucklin ballot, I'd argue, abstaining from the first rank 
shouldn't cause later ranked votes not to be counted. (And I'd argue 
that there is no reason in IRV to not count ballots with a vote in 
second rank, but none if first. The intended meaning is reasonably clear.)

>>However, majority vote and avoidance of all runoffs are two 
>>incompatible goals. So the question is, how important is it that a 
>>majority of those voting support the winner?
>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.

>When there is a cycle its 3 or more members would each be CW if compared
>only with non-cycle members.  For this I claim near-ties since their
>strengths overlap.
>>I'd say it is a bare minimum! We have a defective democracy when we 
>>elect with other than a majority, either of voters directly, or 
>>through chosen representatives. Where representation is involved, 
>>we have a defective democracy even with a majority!
>Plurality NEEDS majority for, if top candidate gets less, another 
>could deserve the win and these voters cannot completely express 
>their desires in their votes.

All methods need majorities to satisfy basic democratic norms. 
Democratic process, in deliberative bodies, generally avoids 
multiple-choice questions; where such questions are allowed, as in 
elections, a majority is required, just as it is with bivalued 
(Yes/No) questions.

>Condorcet has less need, for its voters can rank all the candidates 
>they approve of.

Less need, perhaps. It's possible that the Condorcet winner is a 
winner by a majority over all other candidates. Advanced voting 
systems, in general, can be used as devices to avoid unnecessary runoffs.

But Condorcet methods without some test of acceptance can fail rather 
badly. It could be that the majority would reject the Condorcet 
winner, given a choice of electing the person or running the whole 
election over, and the only reason it appeared that this was the 
Condorcet winner was that, say, voters fully ranked, and some of 
those who formed the majority in some of the wins were actually 
saying that this was the second-worst candidate, which could be pretty bad....

If you are going to use pure ranking, with a single ballot, Cordorcet 
is king, so to speak. But that's an artificial limitation.

I do agree that if a better method is used (like Range or Score 
Voting), a Condorcet test should be used to ensure that the Condorcet 
winner isn't unconciously rejected. A runoff is needed to test this. 
If we have a conflict between a Range winner and a Condorcet winner, 
what has happened is that there may be a majority -- or a plurality 
-- with a weak preference, against a minority with a strong 
preference. Social utility theory would say that the Range winner is 
better; but the votes imply that a majority would reject that winner 
in favor of the Condorcet winner. For reasons I've described many 
times, I claim that a genuine Range winner will prevail in a runoff, 
and that this would be the best result. But occasionally, that would 
not happen, and the Condorcet winner would prevail; what might be 
happening here is that the majority is saying, "No, we do *not* want 
to give up our right of decision as a majority, we don't accept the 
Range results as valid, or, for whatever reason, we, in the majority, 
don't want to make the sacrifice."

And that is their right.

But it won't happen very often....

>Therefore I recommend careful thought as to when runoffs may be 
>worth their expense.

Sure. Little work has been done on this. Some systems require a 
runoff when the margin is less than a certain percentage. That makes 
sense.... Ideally, whatever system is used would predict what would 
happen in a runoff, with reasonable accuracy, and then hold a real 
runoff only when the possibility of a different result is significant.

Looking at the Burlington results, even though Bob Kiss did not gain 
a majority of the votes, as reported by IRV, it's highly likely that 
he'd win a real runoff against the runner-up, Miller, his margin was 
large enough and there is no particular reason for it to disappear. 
In fact, if we look at the second-choice votes, both he and Miller 
gained a majority of first and second-choice votes. My guess is that 
Bucklin would have returned a majority victory for him. IRV concealed 
a lot of votes for Kiss underneath votes for Miller, and a lot of 
votes for Miller underneath votes for Kiss. More Miller votes were 
concealed than Kiss votes: the Kiss supporters were less likely to 
vote for Miller in second place than the reverse.

Were it Bucklin, *some* voters would have truncated, not voting for 
the other frontrunner. But, my guess, most wouldn't have truncated, 
and so Kiss would have still obtained a majority. (There was a lot of 
truncation, bullet voting, even with IRV.)

In the other direction, there were many voters, far more than I 
expected, who *fully ranked,* so fully that they essentially voted 
for every candidate against any write-in. (There was even one voter 
who ranked all the candidates *and* wrote in a name in the last 
place, overvoting that position.) Imagine what would happen if there 
was a serious write-in candidacy in such an environment. These 
full-ranking voters may have just voted for their worst nightmare, 
thinking that by ranking this candidate "last," they were maximally 
voting against him or her.

In this sense, three-rank IRV might be better....

(Burlington had five candidates on the ballot plus one write-in slot, 
hence, because apparently they wanted to allow full ranking, they 
allowed five ranks. The idea is that bottom rank is unexpressed. So 
you could vote for your total favorite in first rank, say, then for 
the best four of the other five candidates. But many voters seemed to 
think that the fifth rank was the bottom, and it's apparent that many 
tried to use burial strategy, bottom ranking the perceived 
competitor, while giving a higher rank to a total joke candidate who 
they would probably be horrified to elect. On the other hand, 
surprisingly many voters *wrote in* a name in the fifth rank.)

>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?

It's not the worst problem. Center squeeze is the worst problem.

More information about the Election-Methods mailing list