Majority Rule and Votes For

[Steve Eppley]

DEMOREP1 wrote:
> Lucien Saumur wrote:
>> I find this scheme artificial. [The scheme being the *votes against*
>> Condorcet tie breaker].
>
>I also find such tie breaker to be artificial. 
>Most average voters would think *votes for* some candidate (or issue
>choice) determines the election result and not *votes against*.

I find it somewhat less intuitive than using margin of difference,
but not artificial.  It meets important standards like majority rule
*better* than methods such as margin of difference.  I suspect that
if I immersed myself in Condorcet examples and considerations, my
increased fluency would alter my intuition.

>The idea that with tie rankings (such as A=B) with x being 0 in a
>Condorcet tie breaker that the votes should not be counted is
>contrary to common sense. 

That's a matter of opinion.  Since this tie-breaker *does* use votes
against and the comparisons are *pairwise*, it *does* make sense not
to count A=B against A or B in the A vs B pairing.  Especially if it
would hurt pairloser(A,B) more than it would hurt pairwinner(A,B).

But the best test of common sense is by how well the method will 
elect the most acceptable candidate.

>The idea that non votes are to be counted twice with x being 1 in a
>Condorcet tie breaker is doubly contrary to common sense.

I basically agree with this.  Though we've discussed x=1, I don't
think anyone has endorsed x=1.

>Condorcet supporters claim that the plain Condorcet method does
>away with strategic voting but they keep bringing up comments about
>the effects of truncation and order reversals in their examples. In
>other words, Condorcet has just as much strategic voting as any
>other voting method.

This makes no sense to me.  The point of the examples has been to
show how strategies *fail* to change the result in Condorcet(0). 
Which means the examples show that there will NOT be as much
strategic voting in Condorcet(0).  Which means that Condorcet(0) 
will meet important standards like majority rule better than other
methods.  Same examples, opposite conclusion.

>Worst of all, plain Condorcet supporters regard majority rule as an
>incidental afterthought being that they keep worrying about the
>lesser of evils (and not about the greater of goods).

This is a misfired attempt at mind-reading.  The point of getting
rid of the dilemma is to elect the candidate that a majority
*sincerely* wants, not a candidate who got a fake majority because
some voters felt compelled to misstate their true preferences. 
Getting rid of dilemmas and opportunities for tactics is to protect
*sincere majority* rule, which is the "greater good."  If a fake
majority is good enough for you, then why not stick with the simpler
Runoff method?

>My conclusion-the Condorcet *votes against* tie breaker falls into
>the category of *wrong majority* methods (along with the MPV,
>approval voting and top 2 in runoff methods).

Incorrect reasoning leads to an incorrect conclusion.  Let's have an
example to illustrate your conclusion, okay?  Let's have an example
where Condorcet elects the wrong candidate and a method you propose
will elect a better choice.

>The remedy to save the concept of head to head pairings is simply
>to call choice voting Choice Voting (with variations for public
>elections, private elections, voter literacy and vote counting
>technology).

A solution seeking a problem?

>The general standard of the average voter is majority rule.

A reasonable standard, except on some issues (like repealing rights)
where voters presumably accept that supermajorities should be required.

Some people believe that voters' preference intensities ought to be
measured, so that a voter with a strong opinion can be "properly"
counted more than a voter with a mild opinion.  These folk don't
have much respect for simple majority rule, which counts a mild
opinion the same as a strong opinion.  (See the apple vs chocolate
example.) Average voters might very well be attracted to methods
like theirs given the choice.  Superficially attractive methods like
these have big strategy problems, though.

>A voter numbers his/her choices, 1, 2, 3, etc. Unacceptable choices
>get a zero (0) vote.
>A majority can with a zero (0) vote defeat any candidate.
>If no candidate survives, then the legislative body can elect the
>executive or judicial officers.
>If 3 or more candidates survive, then there is a divided majority.
>If no candidate beats each other candidate head to head, then the
>*votes for* at the fewest number of choice levels needed can be
>combined until there is a majority winner.
>If there is no such majority winner (due to truncated votes), then
>the legislative body can elect the executive or judicial officers.

What if there's more than one majority winner:
  32: A>B>C
  33: B>C>A
  35: C>A>B
    A loses to C (32 to 68)
    B loses to A (33 to 67)
    C loses to B (35 to 65)
    None beats all others pairwise.  
    (C would win if Condorcet tie-breaker is used.)
  Sum 1st and 2nd rankings:
  A = 32+35=67
  B = 33+32=65
  C = 35+33=68
    More than one candidate has a majority.  Do they all win?
  Sum 1st, 2nd, and 3rd rankings:
  A = 100
  B = 100
  C = 100
    All three are elected unanimously?
Is C the winner, based on the largest majority (68) in the sum of 
1st & 2nd rankings?  To me, this isn't a more compelling victory 
than electing C based on smallest worst defeat.

>If a minority sure to be beaten wants to play strategic games in
>making its first choice (but more likely its second or third or
>later choices - or truncated non-choices), then so what. The winner
>will win with a majority (with the minority having to survive with
>its choice). 

I guess this is an attempt to comply with my request that you analyze 
the effects of voters' misrepresentation of preferences in methods 
you propose.  But saying "so what" isn't a good analysis.  

What I'd expect you to show is that (1) the method you propose will
still elect the *sincere majority* winner given the incentives voters
might have to misrepresent their true preferences, and (2) that the
method won't compel voters to vote some candidate ahead of another 
they prefer (so the candidates' true support can be measured 
accurately).  

I'm not elevating these two standards above majority rule; I'm saying
that I don't think you can protect true majority rule without them. 
(However, even if I didn't care about majority rule, if you simply
said "so what" to my standards I'd be tempted to say "so what" to
yours and we wouldn't get very far.)

With your choice of tie-breaker, wouldn't this create incentives for
some voters to changes their votes so that a candidate who would
have beaten all others pairwise will instead wind up in a circular
tie? With Condorcet's tie-breaker these voters wouldn't be rewarded. 
But how about with this method you've proposed?

One could as well say "so what" about the problems with the Runoff
method, which sooner or later elects a candidate with a majority. 
But you and I would rightly object to Runoff on the grounds that
this Runoff majority winner might not be the sincere preference of a
majority of the voters: using Runoff, fragmentation among similar
candidates can knock them all out of contention during the first
round even if one of them would have had a majority if the other
similar candidates hadn't been running.  The same thing can happen
in MPV, electing with a so-called majority but maybe not with a
sincere majority.

This method you proposed (which could be stated more clearly, but I
think I understand its voting and tallying mechanics) is interesting,
but it needs a better analysis than "so what".  Why not search for
examples showing how it performs better or worse than Condorcet(0) on
the majority rule standard?  

It appears at first sight that the method you proposed will be voted
much like MPV would be voted since in both the early rankings are
fallaciously privileged.  

Suppose, for example, that there are quite a few candidates liked by
a voter more than s/he likes a needed compromise.  Can s/he dare to
rank them all ahead of the compromise (for example, voting
Nader>Sanders>Jackson>Schroeder>Gephardt>Clinton placing compromise
Clinton 6th)?  Since there are so many issue spectra for the voters
and the voters' perceptions of the candidates, it would be risky to
vote sincerely; one can't count upon all the members of the various
majorities not to rank a worse evil than the Clinton compromise
somewhere in their 1-5 rankings.  One would have to think long and 
hard about the possible consequences of ranking Clinton 6th if the 
method treats 6th as a bad ranking.

The voters won't all be counted equally; like MPV this method
fallaciously assumes that a voter who ranks some candidate 2nd like
the candidate more than another voter who ranked the same candidate
3rd.  But a voter who votes A>C may like C just as much as a voter 
who votes A>B>C.

With the method you're proposing (and with MPV) a ballot of {A>B>C
D=0} may actually be *less* of a vote against D than {A>C D=0},
since C may lose to D if the voter ranks C 3rd instead of 2nd.  
A strategy dilemma for the voter, so the voting will be mucked up. 
If the voting is mucked up, then so is the claim to have elected 
the sincere majority preference.

Throwing the decision to the legislature when all candidates are
disapproved may seem capricious and unwelcome by the voters,
especially if they hold the legislature in low regard.  I'd at 
least hope this wouldn't happen before we get a good PR legislature.
Maybe a new election would be better way, if there's time.  You might 
also want to truncate the term of office in these cases.

>Single winner methods are presumably not being done for lifetime
>World Dictator (despite the passion filled Condorcet examples naming
>living persons as if they are in an election for a super powerful
>legislative office) but for ordinary mortals who are in elective
>executive or judicial officers for a limited time. 

True, the stakes aren't as high in a Presidential election as in an
election for Galactic Overlord.  But the stakes are high enough that
voters will feel incentives to vote strategically if the voting
method rewards it.  (Like with the current vote-for-only-one ballot,
when someone who prefers Nader votes anyway for Clinton.  Which is
really a vote against Dole; counting "votes against" won't be a
difficult concept to explain.)  

Providing high stakes examples serves to focus attention on the
strategy incentives that one might accidentally overlook when playing
around with the emotionally insignificant A, B, and C.  And this is a
Presidential election year, so the examples have real-world relevance. 

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