[EM] Does IRV elect "majority winners?"

Abd ul-Rahman Lomax abd at lomaxdesign.com
Wed Jan 7 09:36:09 PST 2009

At 06:14 PM 1/5/2009, James Gilmour wrote:
> > At 07:04 PM 1/2/2009, James Gilmour wrote:
> > >So let's try again, with little bit of additional information that
> > >was (more or less) implied first time.
> > >
> > >At a meeting we need to elect one office-bearer (single-office,
> > >single-winner).  There are four candidates and we decide to use the
> > >exhaustive ballot (bottom elimination, one at a time) with the
> > >requirement that to win, a candidate must obtain a majority of the
> > >votes.  East person is allowed to vote for only one candidate in
> > >each round of the exhaustive ballot and the votes for each
> > >candidate are to be indicated by show of hands.
> > >
> > >First round votes:  A 40;   B  25;  C 20;  D 15.
> > >No candidate has a majority, so we eliminate D.
> > >
> > >Second round votes: A 47;  B 25;  C 20.
> > >It seems that some of those present who voted for D in the first
> > >round did not want to vote in the second round  -  but that is
> > >their privilege.
> > >
> > >QUESTION: did candidate A win at the second round with 'a majority
> > >of the votes'?
>Answer  > Sent: Saturday, January 03, 2009 6:32 PM
> > Yes, A won the second round with a majority of votes.
>So we have made some progress.

Note: "A majority of votes in the second round, which is properly 
considered an independent election."

Note that this process isn't used by deliberative bodies, generally. 
Exhaustive ballot is occasionally prescribed. It's a bad idea, 
precisely because it can suffer from center squeeze. In standard 
deliberative process, there are no candidate eliminations, but 
candidates may and do withdraw. And other candidates may be 
nominated. (My own comment, generally, about close elections, is that 
the best result is probably "none of the above." The best candidate 
wasn't on the ballot!)

>Now let us suppose the meeting decides to hold this election by STV 
>instead of by Exhaustive Ballot (STV = IRV in this single-winner
>case).  Each person has only one vote and is required to show his or 
>her contingency (STV!!) preferences for as many or as few
>candidates as he or she wishes by writing the candidates' names in 
>successive order down a small sheet of plain paper (top = 1 =
>first preference).

You have stated inconsistent conditions: "Required to show," "For as 
many as he or she wishes." That's not a requirement, it's an 
allowance. However, it's true: if the "penalty" for not providing 
adequate ranking is that the voter is deprived of participation in 
further process, which is true for IRV, then we can call it a 
required ranking, with a penalty that isn't as severe as it is in 
Australian where full ranking is fully required.

This limited "requirement" is probably constitutional in the U.S. 
Mandatory ranking isn't, i.e., ranking where the entire vote is 
spoiled if full ranking isn't performed.

>When all the ballot papers have been collected up and the votes 
>counted, we find:
>First stage: first preferences: A 40;  B 25;  C 20;  D 15.
>No candidate has a majority, so we eliminate D and transfer the 
>votes that are transferable on D's 15 ballot papers.
>Second stage: transfer of D's votes: A 7;  B 0;  C 
>0;  non-transferable 8. All 15 ballot papers accounted for.
>Votes totals: A 47;  B 25;  C 20.
>QUESTION: did candidate A win at the second stage with 'a majority 
>of the votes'?

A won the second stage with a "majority of votes" *in that stage.*

This is *not* a "majority of the votes" in the election.

>IF the answer to this question about the STV election is different 
>from the answer above to the question about the Exhaustive
>Ballot, why is it different?

Because, in the first case, there was an election in which the 
majority of those who decided to vote in the election cast a vote for 
the winner.

In the second case, a majority of voters did *not* cast a vote, in 
the election, for the winner.

How many elections were there in the second case? An "election" is a 
collection of votes on a ballot -- or by a show of hands or risings 
or other expression, in a single process of amalgamation.

Again, the second case finds a "majority" of a kind, but not what is 
ordinarily meant by "a majority of votes" when it refers to the whole 
election. You can say, after the smoke clears in the second election, 
that it was won by a majority of votes among the remaining candidates 
after eliminations. The qualification is important and necessary for 
the statement to not be misleading.

"100 people voted in an election, and A won by a majority." Tell me 
what that statement means!

I'd say that it has a clear meaning: 51 or more voters voted for A, 
in some manner.

In Optional Preferential Voting, voters are not forced to vote for 
candidates they may detest. Now, if a majority of voters detest a 
candidate and choose, therefore, not to vote for this candidate, how 
can we then claim that this same candidate won "by a majority"?

No, because that majority was divided in terms of whom it did prefer, 
and because it truncated, perhaps because it detested the two 
frontrunners, -- or, alternatively, didn't have sufficient knowledge 
to discriminate between them -- a candidate *not* approved by a 
majority can win an IRV election.

Certainly it's possible to argue that A should win. But to claim that 
a "majority" has voted for A is to deceive. "Majority rule" requires 
that all decisions be approved by a majority of those voting on the 
question. Normally, wherever possible, the question is confined to 
matters decidable by Yes or No, multiple candidate elections are a 
compromise for efficiency. When a majority of voters vote for a 
candidate, that it was a multiple candidate election is moot. It is 
when majority failure arises that there is an issue, where the 
compromise has a cost, even a significant cost.

The cost is a winner who hasn't been accepted, explicitly, by a 
majority of those voting. Small organizations almost never are 
willing to bear this cost, it can be *very* expensive, it can even 
destroy an organization. Politically, it can set conditions up for 
civil war, if the choice is bad enough and the society vulnerable to this.

People understand and accept being not with the majority, usually. I 
may not like being in the minority, but I can recognize that my task 
is, then, to educate and convince, not to reject the election result. 
But when a majority of people reject an election result, and if this 
objection is serious, you have an unstable situation. If the majority 
organize, or, even worse, some tightly organized minority leads the 
majority in a revolution, we can have social damage that lasts for generations.

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