[EM] Does IRV elect "majority winners?"

Abd ul-Rahman Lomax abd at lomaxdesign.com
Fri Jan 2 14:26:22 PST 2009

At 02:51 PM 1/2/2009, Paul Kislanko wrote:
>I think the cited text provides an important distinction we need to use on
>In theory, we want to discuss election methods based upon how they collect
>and count ballots, which is "analytic" in some sense. As soon as you
>introduce real candidates and party politics (i.e. "strategies") we get a
>real mess that is not so easily analyzed.

Yes. The biggest thing we neglected, going way back, was preference 
strength. In real decision-making, it is crucial, but theorists 
didn't like it, it was messy. It was imagined that "preference" was 
nice and neat. Though it isn't!

>This is relevant to the "how do you define majority?" question because if
>the denominator doesn't include all of the non-voters who dis-approve of
>EVERY alternative it's not a "majority of stakeholders" and in some sense
>you need to count the non-voters, especially if the method discards ballots
>in its "counting rounds."

Sure. It's pretty simple, though: "Majority of the votes" refers to 
more than half of those who voted. We could analyze an election like 
the mess in California a few years back by referring to a "majority 
of votes from those who voted for a Democrat," or a "Republican," or such.

A major point is that most people, asked, want to see majority 
winners. Turns out that, where I have looked, U.S. state 
constitutions required a majority of votes to win, then resorted to 
various devices when a majority wasn't found. We see that with the 
electoral college: if no majority is found, the election goes to the 
House. In New Hampshire, the state House could choose between the top 
two, if I'm correct.

So, people want to see majority winners. Telling them that they will 
get a majority winner from a method means to them that more than half 
of those who voted will have voted, in some way, for the winner. It 
*looks* to a casual observer that IRV will do that. I should have 
known better, but I was actually astonished to see the high 
percentage of majjority failure. It is the bulk of elections that 
didn't find a majority in the first round, with nonpartisan 
elections, and with some partisan ones.

"Majority" is independent of the voting method, though the data must 
be collected to distinguish between support of a candidate and 
merely, with a full-ranking required system, saying that the 
candidate is better than the absolute worst.

Elections aren't merely picking some ideal best winner in a bad 
situation, they are seeking, if a majority is sought, one who will be 
accepted, *at least*, by most voters.

>So, just from a logical perspective a claim to "always select a
>majority-approved winner" must define "majority" in terms of Eligible

That's "absolute majority," and it isn't what we've been talking 
about, except that I have, as part of this discussion, noted the 
effect of preference strength on turnout. Those voters who don't care 
about the available choices don't bother showing up (for better or 
for worse). This exerts a range-like effect on the election, shifting 
results toward those who care. In other words, methods which make 
voting trivially easy might actually worsen results, unless it's a 
Range method, because the factors that make ranked methods, and 
especially Plurality, work reasonably well might be taken away.

>  Or at least define "majority" in terms of voters in the first
>round. So, an IRV winner with 47 votes out of 100 originally cast is NOT a

This is the meaning I've been using, and it is the meaning of 
Robert's Rules, except that they would include a few more ballots 
(informal ballots with no recognizable vote by the rules, but still 
considered to be a "vote.")

For public elections, yes, it's the first-round vote.

>Bucklin is a method that identifies the rank for which a Majority agrees the
>alternative should be ranked at least that highly. No information is
>discarded in the counting process, and no ballots are ignored just because
>the ballots' #1 isn't a plurality winner.

That's right. All votes become equal if it goes to the last round. As 
implemented, it was a plurality method like IRV, but, because all the 
votes are counted, and especially where it's a nonpartisan election, 
there may be votes hidden under the other frontrunner(s), so there 
might actually be a real majority, but it's not reported as moot, 
because the method isn't looking for an overall majority, it's only 
looking for a "last round majority."

Hence, in one San Francisco election, where it was touted that the 
winner will still be required to gain a majority, one Supervisorial 
position was won with less than 40% of the vote.

Most elections where there are runoffs don't find a majority, but 
several have, it happens with elections where the first round result 
is close to a majority. In one election, the reported vote was shy of 
a majority, but it would be a practical certainty that if counting 
had continued, the winner would have had a majority.

>If we make the reasonable assumption that majority be defined in terms of
>the number of eligible voters who cast any (ranked-) ballot at all, we'd
>prefer counting methods that do not discard any of those ballots.
>Just my opinion.

It's the standard meaning. The canvassing method is a different 
matter, though. Robert's Rules describes a method which is IRV as to 
canvassing method, but the majority required for the election to 
complete with a winner continues to be a majority of ballots (other 
than blanks). (The goal is that "one pile contains more than half the 
ballots.") Not half the ballots after rejecting some as exhausted. 
Those exhausted ballots are set into a separate pile, they don't 
choose between remaining candidates, but are still part of "the ballots."

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