Revealing the Majority Winner

[Steve Eppley]

Bart Ingles wrote:
> Blake Cretney wrote: 
> > There is an apparent conflict between my belief that on average
> > preferences towards the end of the ballot are less meaningful, and
> > my support of a method that counts a preference between two
> > candidates independently of where in the ballot the preference is
> > expressed.  That is, if a voter ranks A over B at the beginning of
> > the ballot, the method does not differentiate this from voting
> > A over B at the end of the ballot.
> > 
> > Let me first state that although I have never participated in an
> > election where rankings are allowed, I know I would have trouble
> > ranking many of the lowest candidates.  Elections tend to have
> > a number of fringe or protest candidates who receive little
> > publicity and have little chance of election.  For most voters,
> > a preference between these candidates is likely to be arbitrary.
> > 
> > However, this doesn't matter.  The method I advocate passes
> > MIIAC (Modified Independence from Irrelevant Alternative Criterion).
> > What this states is that any expressed preference between two
> > candidates who are not in the Smith set has no effect.
-snip-

I agree with Blake.  If the voting method satisfies the Smith 
criterion (also known as the "top cycle" criterion, and which 
I assume is also what Blake means by MIIAC) then the effect of 
imprecisely ordering the little-known non-Smith losers is 
intangible.
 
Bart replied:
> I usually think of a fringe candidate as one who is off to one side of
> the spectrum.  My concern here is more about a little-known candidate
> who positions himself in the center, or a charismatic candidate who
> manages to keep from being pinned down so everyone assumes he is in the
> center.  When running against two equally-balanced major candidates, he
> can be the sole member of the Smith set with minimal support of his own,
> if the other voters rank him above what they see as the 'greater
> threat'.

In any major election, the media will do what they perceive as 
their job: providing information about the candidates they 
think have a reasonable chance of winning (and not wasting the 
voters' time with information on sure-losers).  So if/when pre-
election polls show a "little-known" candidate has a chance of 
winning, s/he won't remain little-known for long.

For example, once Perot's chance of winning was perceived as  
significant before the 1992 election, he stopped getting a 
free ride in the media.  The media scrutiny became intense 
enough to reveal his flaws to the voters, and his "soft 
support" fell.  

Someone once said that the prospect of being hanged at dawn 
helps to focus one's concentration.  That analogy applies here.

In less important elections, a candidate might manage to 
remain poorly known to election day, and win, and turn out to 
be worse than the voters expected.  I'm willing to accept the 
possibility of this occasional outcome in exchange for making 
elections more competitive (in other words, giving voters a  
greater number of viable candidates to rank).  Particularly 
since, by making elections more competitive, voters are more 
likely to find better-known compromise candidates to rank 
ahead of poorly-known candidates.  Here's an example:

   A = "left"
   B = "compromise"
   C = "right"
   D = "poorly known"

   Voters whose first choice is A are apt to rank B ahead of D:
      A > B > D > C

   Voters whose first choice is C are also apt to rank B ahead
   of D:
      C > B > D > A

> I'm not saying that this is a likely outcome, but it may not be as
> unlikely as one would expect.  Political factions may tend to equalize
> over time, as the loser shifts toward the center in order to recapture
> votes (examples: Democrats after 1994, Republicans already doing it
> after the last election).  

I agree with Bart about parties' incentive to move toward the 
center in order to get elected.  By using a voting method 
which doesn't deter small centrist parties from being elected, 
this incentive will be even greater.  That means there will be 
a number of *well-known* candidates (and parties) trying to be 
in the center of the voters, which I believe will make it less 
likely that a majority of voters will rank an unknown ahead of 
all the well-known centrists.

A poorly-known centrist will probably be majority-ranked as 
less preferred than some well-known centrist.  And a poorly-
known candidate who is perceived by most as off-center will be 
ranked even worse by a majority.  

So I think Bart is overly concerned with the possibility that 
in an important election, some poorly-known jerk will appear 
to liberals to be liberal and appear to conservatives to be 
conservative, escape scrutiny of the press, win and be 
disastrous.  To me this possibility looks negligible.

> The more equal these factions, the less overall support 
> required to be the Condorcet winner.

I think the term "support" here is being (mis)used 
inconsistently with Bart's point about poorly-known 
candidates.  Nearly everyone misuses the term--it's often 
taken to suggest something absolute, but the phenomenon to 
which the term really refers is a relative pairwise 
preference.  

The number of voters who rank a candidate first is NOT a good 
measure of "support" or "strength."  Even IRO advocates should 
agree with me, since they agree that B should be elected here:

   49: ABC
   13: BAC
   13: BCA
   25: CBA

   IRO advocates count the 25 ballots which ranked B second as 
   heavily for B (in the final pairing against A), as the 26
   ballots which ranked B first.  That makes sense to me, but
   is inconsistent with claims that "absolute support" exists
   and is measurable by absolute rank position.

Support doesn't really exist in an absolute way, and is 
sensible only relative, pairwise, to other alternatives.  For 
instance, suppose a voter's preference order is A>B>C but A 
chooses not to compete.  It's not sensible to claim that the 
voter's support for B relative to C is reduced by the presence 
on the ballot of more preferred alternatives, or increased by 
the absence of more preferred alternatives.  And it is equally 
silly to claim, as does the CV&D definition of IRO, that 
transferring votes from a candidate eliminated due to alleged 
"weakness" somehow makes remaining candidates "stronger."

Perhaps it would be better to speak in terms of "hard" versus 
"soft" relative preferences rather than "support"?  We can 
define a soft preference as a preference based on little info 
about the preferred candidate, which would change if the voter 
is given more info about that candidate.

But the information in preference order ballots doesn't 
indicate how well-known the candidates are to the voters.  
(Nor does it indicate anything about absolute "support.")

I believe it's folly to try to impose criteria intended to 
defeat candidates who are poorly known or who have "weak 
absolute support" when tallying preference orders, since 
preference orders don't contain information about that.

-snip-
> Maybe the Condorcet criterion should be balanced against
> other criteria.  Intuitively, I tend to think a very weak 
> Condorcet winner

Similar to my comments above, I have trouble with the term 
"weak" here.  It suggests something absolute when all we have 
in the ballots are relative preferences.  The so-called 
"strength" of "support" will appear to fragment when 
additional candidates are nominated to the ballot, so if it is 
used to determine the outcome then it will induce a "lesser of 
evils" dilemma.

I'll go along with using of the term "weak" to refer to a 
little-known candidate, which is what Bart was writing about 
at first, but preference orders will not indicate how well-
known a candidate is.  I disagree with any attempt to link 
"absolute strength" with the number of voters who rank a 
candidate first.

> should be dropped & those votes used as a tiebreaker to find the AV/IRO
> winner; on the other hand, I would drop both CW and AV winner in favor
> of the Plurality winner (A) in a situation like:
> 
> 20  A
> 1   B C ... Z
> 1   C D ... Z B
> 1   D E ... Z B C
> .
> .
> .
> 1   Y Z B C ... W X
> 1   Z B C ... X Y
> 
> even though one of the other candidates would have 25 votes in the final
> round (under IRO), vs. the plurality winner's 20.

I don't see a compelling reason to elect A here, since a 
majority prefer any other candidate more than A.  Also, A is 
the last choice of a majority, an excellent reason to defeat 
A.  Plurality is the ONLY method I can think of which will 
elect A here!  Bart has fallen into the intuitive trap of 
trying to measure "absolute support" given relative 
preferences.

(Incidentally, I would expect in practice that the other 
potential candidates, and/or the voters, would defeat A by 
working to build a coalition for another candidate, in the 
traditional ways.  If done by the other candidates, this would 
mean that all but one non-A candidate would withdraw or not be 
nominated.  If done by the voters, it would mean they'd 
misrepresent their preference orders to rank a particular non-
A candidate as first choice.)

It seems a reasonable interpretation of the above example is 
that candidates B..Z are essentially clones of each other.  
Just because they fragment the majority who prefer them more 
than A doesn't mean they have "weak support."  They are all 
majority-supported relative to A.

I'd sooner have faith in the voters and the media to make sure 
that candidates who have a significant chance of winning do 
not remain little-known by election day, instead of advocating 
a voting method which defeats compromises when three or more 
viable candidates compete.  Methods like plain IRO and 
Plurality deter reasonable candidates from competing due to 
the candidates' rational fear of fragmenting votes needed to 
defeat worse alternatives.  Both methods will maintain the two 
party, one nominee per party, system, and maintain the need 
for primary elections.  IRO will be less marginalizing of 
third parties than Plurality, but only up to a point: with IRO 
a voter who prefers a third party's candidate will only be 
able to rank that candidate first when s/he is confident that 
favorite will be eliminated before the needed compromise 
candidate is eliminated.  When a third party candidate grows 
strong enough (moves close enough to the center) that it 
manages to eliminate the needed compromise (i.e., the more 
preferred of the two viable candidates), then IRO backfires by 
electing the least preferred of the two big tent parties.

On the other hand, if candidates are permitted to withdraw 
"just in time" (after the votes are cast but before the tally 
is final), then obviously they will not be deterred from 
competing, since they can "unfragment" the votes when 
necessary to defeat a "greater evil."  This option can 
mitigate even a flawed method like IRO (and even plain 
Plurality, if the voters vote preference orders so each ballot 
can be counted for its most-preferred non-withdrawn 
candidate).  And it would appear to reduce or eliminate 
incentives for voters to misrepresent their preference orders.

Here's something to consider while on your way to a better 
understanding of the relativity, not absoluteness, of 
"support":  Suppose the voting method is IRO modified to allow 
candidates to withdraw just in time, after the voting.  
Suppose the votes are:

   46: ABC
   10: BAC
   10: BCA
   34: CBA

If no one withdraws then IRO will elect A (defeating the 
Condorcet winner B).  But C would choose to withdraw just in 
time, in order to prevent A from being elected (assuming that 
C's preference order is CBA, which seems reasonable), so IRO 
will actually tally these ballots:

   46: AB
   10: BA
   10: BA
   34: BA

and elect B, the centrist compromise.  In other words, C would 
throw his/her "support" to those supporters' next choice, B, 
revealing B's true majority "support relative to A".

If B were little-known and actually a jerk, then perhaps C 
would not choose to withdraw, recognizing the voters' soft 
(and misguided) preference for B over A.


---Steve     (Steve Eppley    seppley at alumni.caltech.edu)