[EM] Winning-votes vs margins as a measure of defeat-strength

MIKE OSSIPOFF nkklrp at hotmail.com
Mon Dec 22 01:54:01 PST 2003

For Condorcet's method, I recommend that the strength
of pairwise defeats be measured by "winning-votes"
(wv). Winning votes says:

If X beats Y, then the strength of that defeat is measured by the number of 
people who ranked X over Y.

[end of definition]

Some others advocate using margins of defeat instead.

Here's why winning-votes is better.

Below is something that I send out to answer that question. But let me 
briefly say that one problem of margins is that the subtraction that it 
involves erases information about majorities, which is why margins has 
majority rule failures that wv doesn't have. One result is that wv meets the 
majority defensivse strategy criteria, SFC, GSFC, WDSC, and SDSC; and 
margins fails all those criteria. They're criteria intended to measure for 
the standards of majority rule, and minimizing need for defensive strategy. 
The definitions of those 4 criteria tell how complying methods (wv 
Condorclet) avoid certain avoidable defensive strategy needs.

Thoes criteria are defined at:




But there's also a basic ethical reason wv acts more justly than margins 

When every candidate has a pairwise defeat by another
candidate, Condorcet's method, in all its versions,
solves that problem by sequentially dropping the
weaker defeats--or by sequentially keeping the
stronger defeats.

When everyone has a pairwise defeat, and we have to
elect someone anyway, then that means that we have to
ignore or disregard or overrule someone's pairwise
defeat(s)--when we elect someone in spite of his
having a pairwise defeat, a public statement that the
voters prefer someone else to him. So Condorcet has to choose which defeat 
to drop.

But dropping or ignoring a defeat is not something to
be taken lightly. It means that we're disregarding,
overruling, a statement made by the voting public,
when they indicated that they preferred one candidate
to another. And when we overrule that public choice,
we're overruling those voters who won that public

Suppose that, in the pairwise comparison betwen D & B,
D beats B, 60 to 50, meaning that 60 people ranked D
over B, and 50 people ranked B over D.

If we drop that defeat, overrule that public statement
that D is better than B, then we're also overruling
the 60 voters who won that public vote about that
2-way contest between D and B.

We want to minimize the number of voters whom we
overrule. So we measure the importance of a defeat by
the number of people who voted for that defeat.

Now, sometimes someone will say: But if you keep that
defeat, doesn't that mean that you're overrule the 50
voters who voted against it, the 50 voters who ranked
B over D? No! Those 50 voters were overruled by the
public vote in which the voters collectively said that
they prefer D to B. The only way that the voting
system overrules a public decision is when it drops a
defeat, when it overrules a public decision for one
candidate over another. We're not doing that when we
keep a defeat that the public chose.

That's why winning-votes (wv) is more democratic than
margins, more ethically fair.

But there's another reason why we prefer wv to
Nash Equilibrium:

A Nash equilibrium is an game outcome in which no one
player can improve the result for himself by changing
his play, if no one else changes their play.

In voting system discussion on the election-methods
mailing list, a "player" is taken to mean a
same-voting set of voters.

With the kind of Condorcet that measures defeats by
margins, as with IRV and Plurality, there are often situations
(configurations of sincere voter preferences) in which
the only Nash equilibria are ones in which some voters
vote someone over their favorite in order to protect
majority rule or protect the win of a Condorcet
candidate (a candidate who, when compared separately
to each one of the others, is preferred to him/her by
more people than vice-versa).

With Approval or wv Condorcet, every situation has at
least one Nash equilibrium in which no one reverses a
sincere preference.

Mike Ossipoff

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