[Election-Methods] RELEASE: Instant Runoff Voting (Chris Benham)

[Abd ul-Rahman Lomax]

At 12:55 AM 6/23/2008, Chris Benham wrote:
>Kathy,
>
>Imagine  that  Approval is used to elect the  US President and
>as in the current campaign the Republicans  are fielding one
>candidate, McCain.  Does that mean that the big fight for the
>Democrat nomination between  Clinton and Obama we've just
>seen would in the Approval scenario be completely unnecessary?

No. That fight is over the Democratic Party nomination and 
endorsement. It means that the whole apparatus of the Democratic 
Party is devoted to one candidate, which is, of course, strongly in 
the interest of the Democratic Party.

>Why not simply endorse both candidates?  After all, one cannot
>possibly spoil the election for the other because Approval has
>no spoiler problem. Voters simply approve candidates or not
>completely regardless of what other candidates are on the ballot,
>right?

Sure. If we imagine that somehow the parties have decided not to 
nominate candidates, snowballs in hell nevermind, running both Obama 
and Clinton against a single McCain would probaby result in very 
common double-voting. Now, if Obama and Clinton heavily campaign 
against each other, slinging mud, etc, trying to convince the voters 
that the other one is practically the devil, nobody would benefit 
from this except McCain. Which is quite why we don't do things this 
way. Parties in Australia don't run multiple candidates for the same 
single-winner office, do they?

The problem, were it Approval, wouldn't be so much the voting method. 
(Which, by the way, loses most of the problems it has if a majority 
is required or there is a runoff). It would be the rest of the 
system, the process by which voters become informed, or deluded, 
depending on your point of view.

>I  think that in practical effect Approval  does have a "spoiler" or
>split-vote problem  that would be sufficient for the Democrats to
>still want to endorse one candidate only.

There are *lots* of reasons why the Democrats would want to do that. 
Or any party. This is a red herring argument. The "split vote 
problem" in Approval is a very different animal than the split vote 
problem in Plurality, or, for that matter, in IRV.

>What I actually wrote in my initial post on the 5  "fairness
>principles in your paper (regarding IIA):
>
>In practical effect  *no* method meets this.Approval and Range can 
>be said to meet
>Independence of Irrelevant Alternatives (IIA) only if the votes are 
>interpreted as the voters giving
>ratings on some fixed scale that is independent of the actual candidates.

No, that's not correct. Perhaps it would be useful if you actually 
state the version of IIA you are using. Usually, it refers to adding 
or subtracting a candidate without changing the "preference order" of 
the other candidates, but if you are going to use it with Range and 
Approval, you have to modify it; the basic modification is that the 
Range Votes or Approval Votes don't change, and all that happens is 
that a new candidate is added to the ballot or taken off the ballot.

If voters are allowed to actually change their votes, *no method 
meets IIA.* Simple proof: there is a candidate whose name is a 
trigger for a long-hidden internal program that causes human beings 
to fall into a trance when they contemplate whether or not to vote 
for a candidate, and they leave the booth with false memories of what 
happened (really happens with trance, sometimes, i.e, false memory). 
The voters see this new name on the ballot, and regardless of how 
they would have voted, they become incapable of voting, so all 
candidates tie with no votes. And thus the winner could change.

>On this perverse interpretation Approval and Range do not reduce 
>to  FPP in the 2 candidate election,
>in violation of  Dopp's "fairness principle 4":
>
>"Any candidate who is the favorite [first] choice of a majority of 
>voters should win."
>
>(approval or non-approval counts as "rating" on a 2-point  scale).

Chris, you should look at Dhillon and Mertens, "Relative 
Utilitarianism," where they purport to prove that Range Voting is a 
unique solution to a version of Arrow's voting axioms that 
accommodate Range Voting. Relative Utilitarianism refers to "votes" 
which are "normalized von Neuman-Morgenstern utilities in the range 
of 0-1. I.e., Range Voting. Warren Smith is actually not in outer 
space on this (their work preceded his).

Because of the normalization, in the two candidate case, Majority is 
satisfied. Because vN-M utilities are modified by probabilities, it 
gets complicated in the three-candidate case, where RU is considered 
the unique solution. If I remember correctly. I'm hoping to help get 
a popularization of Dhillon and Mertens prepared, it's needed. Smith 
calls their use of symbols "Notation from Hell." And he's familiar 
with the conventions!