[Election-Methods] RELEASE: Instant Runoff Voting - Not What It Seems

[Chris Benham]

Hello,
Since I regard  "IRV" (the Alternative Vote, unlimited strict ranking "version") as 
one of  the good methods, the best in my judgement of the methods that meet
Later-no-Harm, I am encouraged to respond  to Kathy Dopp's anti-IRV propaganda
piece.


Some Fairness Principles for Voting MethodsConditions have been proposed to judge 
whether or not voting and vote-counting methods result in fair or in non-fair, paradoxical 
election results.

1. The addition of an alternative (candidate) who does not win should not affect the outcome.
If you have an election contest where candidate A wins, and you introduce a new candidate C,
then either candidate A should still win, or candidate C should now win. In other words, spoilers
should not be possible or the addition of an alternative (or candidate) that doesn't win should not
affect the outcome.

This is some times called "independence of irrelevant alternatives" that says that the collective
preference order of any pair of alternatives x and y must depend solely on the individual voters'
preferences between these alternatives and not on their preferences for other irrelevant (nonwinning)
alternatives.
IRV does 
elections where "spoilers" determined who won, neither does the existing plurality voting
method meet this condition.
do seem to meet this fairness condition.not meet this condition of fairness. (See appendix A.) As we’ve seen from prior U.S.ix Other alternative voting methods, such as approval or range voting


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. 

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

I don't see what IIA actually has to do with "fairness". To me it is only about congruity or 
mathematical elegance.
2. 
must be preferred to alternative y in the collective preference order
result]. This is some times called the "Pareto condition" that says whenever all individuals prefer
an alternative x to another y then x must be preferred to y in the collective preference order. It is
possible to find examples of when IRV and plurality voting violate this fairness condition.Whenever all individuals prefer an alternative x to another alternative y then alternative xx [the final election

No it isn't.  And why in a single-winner election method do we care about the whole "collective
preference order"  instead of just the winner?

(See appendix B.)

There is no example of IRV or  plurality voting failing Pareto in appendix B, only one of  Approval
meeting it.3. The candidate who wins should have received a majority of voters’ votes.Some jurisdictions require winning candidates to have a majority (more votes than 50% of the
ballots cast by voters).


Maybe so, but should they?  I gather that if this requirement isn't met, the decision on who
fills the office is taken out of the hands of the voters.  Some voting methods, such as plurality voting and IRV 
condition. Actual top-two runoff elections do.do not meet this


Only if "voters" means only those who showed up for the second round. Say in a 3 candidate
election, I can't see any justification for making this big distinction between a "majority" in the
second round of  Top-Two Runoff (TTR)  and the majority of voters who participate in the 
second round of  IRV.

Kathy, do you insist that the election method requires voters to make second trip to the polls
whenever the first doesn't produce a winner who "receives a majority of voters' votes"?

Two-round methods can have their plusses, but in general I think it is more appropriate to
compare IRV only with other decisive single-round methods.

But while we're here, IRV (Alternative Vote, unlimited ranking)  dominates TTR in terms of
criterion compliances, including those that relate to  "majority rule".  Both TTR and IRV 
meet  Condorcet Loser, but IRV (Alt.V, unlimited ranking) has the extra advantages over 
plurality voting (FPP) of meeting Majority for Solid Coalitions (aka Mutual Majority), Mutual
Dominant Third, and  Clone-Winner.

4. 
IRV does not always pick a majority winner out of all ballots cast, IRV proponents emphasize
that 
candidate as the winner. However, the existing plurality voting method also meets this condition,
which IRV proponents call the "majority criteria".Any candidate who is the favorite [first] choice of a majority of voters should win. Whileif a majority winner exists among voters’ first choices, then IRV will always select this



I think some call this the "Majority Criterion" ("criteria" is the plural of *criterion*).  I and others 
prefer the name "Majority Favorite".  It isn't of much idependent theoretical interest to me.  It 
is implied by Majority for Solid Coalitions and Mutual Dominant Third, which are met by IRV 
(Alt.V,unlimited ranking) but not TTR.  Also it is implied by the Condorcet Criterion.

It is FPP's one redeeming feature compared to Approval (and more clearly, Range). It is failed
by  Borda.Range and approval voting do 

That's right. Obviously this has to be the case  to maintain compliance with Later-no-Harm.
Kathy, is Majority Favorite a "fairness condition" you support or not?


The pair-wise favorite among all voters should be the winner. In other words, the candidatenot meet this condition.

This is the Condorcet criterion.  It is a strict technical pass/fail test. I agree that it is good for
methods to meet it, but it is incompatible with both  Later-no-Harm (as met by IRV and FPP)
and  Favorite Betrayal  (as met by Approval, Range, and a version of Bucklin).
In my book a method can fail the Condorcet criterion and still qualify as "good" if it meets
some useful criterion that is incompatible with it.So, IRV does 
methods are available that meet more of these fairness conditions.not meet four out of the above five fairness conditions and other alternative voting

This is a very weak argument. There are very many reasonable/interesting/plausible standards/
criteria/properties  that have been applied  to assessing voting methods one could select from
to present an arbitrary list of  "five fairness conditions".  For any method it is very easy to make
such a list so that the method only scores 2/5.
This particular list is a very unimpressive grab-bag. The first two have been inappropriately
borrowed from Arrow's Impossibility Theorem.  The first is (in practical effect) met by nothing
and the second is met by every remotely reasonable deterministic method.
The third is something very silly that no decisive one-round method that allows truncation can
meet.  The fourth is  is very untaxing, and mainly of  some interest to supporters of  IRV and
FPP who dislike Range and Approval.
The fifth is serious. It implies the fourth.  
If these five were the only possible  "fairness conditions" or clearly the most important and it 
was obvious that they should be given approximately equal weight, then IRV's low score of  2  
(not 1) out of 5 might  suggest that it isn't a good method.

Probably more later,

Chris Benham


http://electionarchive.org/ucvAnalysis/US/RCV-IRV/InstantRunoffVotingFlaws.pdf

© 2008 Kathy Dopp/National Election Data Archive. A non
royalty bearing license allowing one time use of this material is granted, under the condition that a copy of whatever use
is made of this material is sent to kathy.dopp at gmail.com and kathy at electionarchive.org when it is first disseminated,
and full attribution is made to Kathy Dopp/National Election Data Archive along with this document’s Internet URL
5. 
preferred when compared pair-wise over other candidates by the most number of voters should
win. This is called the Condorcet winner. Both plurality and IRV do 
Range and approval voting meet it more often, as in the examples in appendix A.not meet this criterion. The majority criterion candidate wins in 
IRV even if the candidate is the last choice or disapproved of by all other voters, and even if there 
is an alternative candidate who is approved of by all voters.


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