[EM] Does IRV elect "majority winners?"

[Abd ul-Rahman Lomax]

At 07:04 PM 1/5/2009, James Gilmour wrote:
>It is quite clear (and now agreed) that the winner (A) of the 
>Exhaustive Ballot example had "a majority of the votes" at the second
>round and so was the rightful winner of that Exhaustive Ballot.  But 
>it would quite wrong to say that candidate A had the support of
>the majority of those who had taken part in that election, because 
>there were two rounds in that one election and some who voted in
>the first round opted not to vote in the second round.

The error here is in describing exhaustive ballot as if it were a 
single election. It isn't. It is a series of elections, with the 
candidate set for each increasingly restricted.

It's a bad idea; if it's practical to hold a series of elections like 
that, why not simply hold them, without forced elimination? Sure, *in 
theory*, the series could then go on forever. In practice, though, it 
terminates, eventually the voters get it together and figure out the 
best compromise and vote for it.

Now, if it is a deliberative body, with motions in order, a member 
could always rise and move that an eliminated candidate be restored. 
A majority could *force* this (a majority can effectively suspend a 
rule like an elimination rule). So a Condorcet winner would *not* be 
eliminated, if the voters cared sufficiently to make that motion and 
stand behind it. They could also, by a majority, eliminate candidates.

Better voting methods simulate this process better.

And *preference strength matters.* This is what so many of us have 
missed. Ranking doesn't contain adequate information to predict what 
will happen in deliberative process. A>B, fine. Now, *how likely is 
it that this voter will *change his or her mind*? I.e., vote A=B or 
even B>A? It depends on preference strength!

"candidate A had the support of
the majority of those who had taken part in that election, because 
there were two rounds in that one election and some who voted in
the first round opted not to vote in the second round."

Is this wrong? Sure, as stated, it is, because we can figure out from 
the context that "the election" means the entire process, which is 
actually two elections.

Under Robert's Rules, the original election *fails* and becomes 
totally moot. There could be *many* elections. The papal election 
rules required a 2/3 majority and Open Voting (approval) was used. It 
sometimes took a lot of polls. Given all those polls, would we say 
that 2/3 of those who took part supported the winner? Sure, we would. 
"Took part" means that they voted in the final poll.

When a matter is voted on repeatedly, and we then talk about the 
result, we talk about the *final* result, and the number of votes and 
the results of the earlier polls, which failed to find the required 
quota, are moot.

James, you are stretching pretty far. Why?

>So here we have an important difference between "a majority of the 
>votes" and "a majority of the voters".  But neither is (or should
>be) of any relevance to the detailed voting system rules for an IRV election.

Want to talk about "the votes" in IRV elections? How many "votes" are 
there? Sure, only one vote is active at a time, but there are *many 
votes* cast. Look at Burlington; the vast majority of votes cast, as 
alternative votes, were never counted at all.

The Minnesota case, Brown v. Smallwood, following an earlier case, 
notes that it is a majority of voters which counts, not votes. 
However, they then proceed to count the number of votes, with 
apparent concern that with Bucklin, there are more votes than voters. 
*This same argument* applies to IRV, in fact. It was an anomalous 
decision, not sustained anywhere else in the U.S. IRV allows voters 
to cast more than one vote; the particular nature of the rules means 
that only one of these votes is active in each round.

Bucklin allowed more than one vote to be active in each round, but 
there is still only one vote cast in any pairwise election -- or two, 
which is the same in effect as none -- and, in the end, only one vote 
from each voter contributes to the outcome, *all the rest could be 
eliminated without changing the result, but only the margins.*