Hugh's vote for Smith//Condorcet

Steve Eppley seppley at alumni.caltech.edu
Tue Jul 9 11:46:50 PDT 1996

```There are a couple statements in Hugh's ballot explanation for which
my understanding differs, so I want to explore them.

Hugh Tobin wrote:
-snip-
>In Smith//Random the temptation to strategic voting would be least,
>because success in creating a circular tie would generate at best a
>one-third chance of electing one's first choice.

Those odds (1/3) may be enough of a temptation.  It's true there
would also be a 1/3 chance of electing an even worse candidate, but
what about the cases where the voter thinks the sincere-Condorcet
winner is nearly as bad as the worse candidate?  Suppose a voter
has the following opinions on the three candidates Left, Middle,
and Right, expressed on a scale of -10 to +10:
L= +10, M= -8, R= -10
And suppose the pre-election poll data indicates M will beat both the
others pairwise if voters vote sincerely.  If M wins, this voter
evaluates the outcome as -8.  If there's a random draw, this voter's
expectation is (1/3 * +10) + (1/3 * -8) + (1/3 * -10) = -8/3.  This
is much better than -8.  So why shouldn't this voter order-reverse,
voting L > R > M in hopes of creating a circular tie?

And what will the supporters of the other candidates do?  Some will
be aware of a lesser of evils dilemma: the supporters of R may feel
scared to vote sincerely (R > M > L) because of the possibility that
L will randomly win a circular tie, so they may use the defensive
strategy of voting M more preferred than their true preference.

It's hard to quantify how often there will be strategic voting
in Smith//Condorcet and Smith//Random.  To me it looks like
Smith//Condorcet (and Condorcet) will have the least, not
Smith//Random, because the "votes against" tiebreaker is such a
good deterrent.

-snip-
>A priori, without knowing how a particular election will come out,
>that larger majority might prefer a system in which the middle
>voters have to choose one wing or the other, over a system in which
>a candidate with a narrow core of support from a special interest
>could insert himself between the major parties on the main issues of
>the day, and prevail as each wing's lesser evil (Condorcet winner),
>while extracting benefits for the narrow core constituency as the
>price of compromise.   Therefore -- at least on the assumption that
>sincere voting would be the norm, or that insincere voting in IR
>will only reduce the incidence of different outcomes than SC would
>produce -- it does not seem inherently irrational or undemocratic to
>prefer IR over SC, but it implies a greater desire for decisive
>outcomes on major issues. This means a willingness to forego
>compromise and accept the risk that the "greater evil" will prevail.

This argument (that maybe the electorate would prefer a system which
forces a small middle to pick one of the wings) is interesting, but
I don't think typical IR advocates use it.  I think most would
consider it to be a failure of the method if a candidate who would
beat all others pairwise loses, but they like IR anyway based on its
alleged simplicity/familiarity and a belief that such failures won't
happen often.

>It has not been shown that adding Smith makes Condorcet any more
>subject to manipulation, or has any other defect, unless I missed
>something.

Unless you consider the added complexity of its definition to be a
defect.

>The question is whether the value of the deterrent effect of
>Smith//Random upon order-reversal strategy outweighs the appearance
>of casino democracy and the intuitive unfairness of giving a
>candidate in the Smith set who lost one pairwise contest by a
>landslide the same chance as one who lost one by a bare majority.
>On balance I think not, despite item 9, below.  But if, under SC, a
>significant number of races were to degenerate into order-reversal
>manipulations or confusing and deceptive claims about how to elect
>circular tie, then Smith//Random could be the remedy.

As I wrote above, I believe S//R would have more strategic voting
than S//C, not less, so S//R would be the opposite of a remedy.  If
there's a candidate who would beat all others pairwise if the voters
would vote sincerely, S//C will still tend to elect this candidate
even when another candidate's supporters misrepresent their
preferences.

>9.  In Smith//Condorcet (or plain Condorcet), I am not convinced
>that opportunities for strategic voting in a 3-way race would be so
>rare as to be a trivial consideration.  Unless I misunderstand, the
>"truncation" antidote to order-reversal offered by Mr. Ossipoff is
>a deterrent that depends on the credibility of a threat by the
>Condorcet winner that his supporters will vote in a manner (refrain
>from ranking their true second choice) that cannot help elect their
>favorite but can help elect their least favored candidate, just to
>punish the supporters of their second-favored candidate.  This
>threat may lack credibility.

I've forgotten this scenario; can you post a relevant example?
Here's the example I remember:
The ballots:
45: D>N>C   <-- reversal
20: C
35: N>C>D
The pairings:
D<C    (45 to 55)
C<N    (20 to 80)
N<D    (35 to 45)
N wins the circular tie using Condorcet (only 45 against in N vs D).
The N supporters didn't have to change their votes to counter the
D supporters' reversal; the reversal is already deterred by Condorcet.

>In each pairwise contest between X and Y, count as 1/2 vote for X and
>1/2 vote for Y an equal ranking of X with Y by a voter, if that voter
>ranked all other members of the Smith set ahead of X and Y.
-snip-

This proposal is new to me.  I think we should spend time examining
it.  It would certainly complicate the definition of the method, and
considerably increase the time it takes to tally the ballots (since
it requires an extra pass to calculate the Smith set before the tied
rankings), but perhaps its properties are important enough to justify
that.

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

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