[EM] Does IRV elect "majority winners?"

[Abd ul-Rahman Lomax]

At 05:46 PM 1/5/2009, Juho Laatu wrote:
>It is possible that the voters would have
>liked to take position but for some reason
>did not know which candidates would be the
>strongest in this election. This situation
>is the same for all methods. A second round
>could improve things. But it may be that
>it is enough if the method offers the
>voters the option to indicate their opinion.
>This should be fair enough, at least if the
>number of the candidates is reasonable (not
>e.g. 100) or the leading candidates are
>well known so that all voters can evaluate
>those key candidates if they want to do so.

Voters may need more information to rank candidates. The problem of 
limited voter knowledge was recognized by Lewis Carroll, in a 
pamphlet published in 1884, as a weakness of STV; many voters know, 
quite well, their favorite, but don't know much more than that. Is 
there a minor candidate who is better than the other frontrunner? 
Lower preference votes contain a lot of noise, but it is noise which 
is spectrally affected by matters such as name recognition. I think 
that this is the reason why IRV in nonpartisan elections tends to 
closely reproduce Plurality results.

Suppose we have an election where X% of voters prefer A over all 
others. Let's assume that this is a plurality. Now, eliminate 
candidate B from the election. What percentage of voters prefer A 
over all others? It turns out that the supporters of candidate B, 
that preference excepted, are more or less a representative sample of 
the rest of the population, so, roughly, X% of them prefer A over all 
remaining candidates. The absolute gap between A and the rest simply 
widens with vote transfers. However, voters without adequate 
knowledge may have truncated, so A may not make it to a majority. 
Only in close elections would we expect to see a "comeback" election, 
where the runner-up in the primary or first IRV round ends up 
winning. Apparently, in Australia, it never happens that the third 
place candidate ends up winning.

In other words, one could probably save a whole lotta countin' by 
doing batch elimination.

Yet we also know that third place candidates in primaries might very 
well win a real runoff. The Lizard v. the Wizard. Chirac v. Le Pen. 
These were both major runoff elections where the probable Condorcet 
winner -- and a stable one -- would almost certainly have won a 
direct runoff between himself and either of the actual runoff 
candidates. Rules prevented write-ins.

To some extent, folks, we -- and many others in academia -- have 
allowed ivory-tower preoccupations to distract us from what is really 
going on in real elections. The theoretical desirability of 
deterministic elections, the holy grail of the ideal single-winner 
deterministic system, led us down the wrong path and made much of our 
theoretical work practically useless.

We *must* understand what is going on with runoff systems.

Note that small democratic bodies use a simple majority requirement 
to great effect. With simple Plurality voting and a majority rule, 
and no candidate eliminations, but voluntary withdrawal and voter 
shifts in voting patterns to accomplish compromises, they elect 
Condorcet winners efficiently (or a candidate with utility close to 
that of the Condorcet winner) and usually quickly. But not with a 
single ballot, in some cases.

Consider what it would be like if we wanted to build a computer to 
make decisions. If we require that the decision be made instantly 
based on input, in one processor cycle, we must build one very 
complex computer. But if we allow the computer to iterate, it can be 
much simpler. *Much* simpler, a Turing machine.

If the input is human communication, the single-cycle computer can't 
even approach what an interactive process can do, where, essentially, 
questions are asked that are dependent on the results of previous questions.

This is Robert's Rules of Order's criticism of the STV method: not 
only can it fail to find what they call a "compromise winner," which 
is basically a Condorcet winner, which is a pure methodological 
failure, other preferential voting systems are far better at this -- 
even though IRV probably gets it right 90% of the time *as does 
plurality*, partisan elections excepted -- but it "deprives" voters 
of their right to base votes in a subsequent election on the results 
of the previous one. Remember, RRONR is assuming election *failure* 
and not a reduced candidate set in the succeeding elections.

This is like Approval theorists who consider cycles of polls, where 
voters, realizing that in order to complete the election, they must 
lower their approval cutoffs, do so, until one candidate has a 
majority. That's what Bucklin does, effectively, as a method, but 
it's hindered by bullet voting, *which is normal and which must be 
expected.* Runoffs fix this problem, and if voters don't like having 
to vote again, they can take steps: add additional preferences!