[EM] Debian pairwise voting (fwd)

[Rob Lanphier]

Mail from Mike O. regarding the Debian pairwise voting...
---------- Forwarded message ----------
Date: Fri, 04 Feb 2000 03:51:43 GMT
From: MIKE OSSIPOFF <nkklrp at hotmail.com>
To: robla at eskimo.com
Cc: nkklrp at hotmail.com
Subject: Debian pairwise voting


Hi--

If the Debian rules are strictly followed, then, by rule 3,
all options that are dominated [pairwise beaten] by at least one
other option are discarded, and references to them in the ballot
papers will be ignored.

That means that unless there's an "undominated" alternative
("option"), every alternative will be discarded and deleted
from the ballots.

Rule 4 provides for electing the alternative that dominates
all others, if there is one, and rule 5 says what to do if there
is more than 1 option remaining--but there will never be more
than zero options remaining unless there'd been a BeatsAll winner,
a candidate who "dominates" every other candidate.

So the rules need work. Rule 3 should be dropped. Rule 5 should
just start with "If there is no undominated option, then..."

***

With pairwise voting, it makes all the difference how circular
ties are dealt with. When Instant Runoff (they call it 1-winner
STV) is used to solve circular ties, that means that the group
of voters who are in a position to make a circular tie, by
order-reversal, or by truncation, sincere or strategic,
are also the group that has an automatic win if they do make
a circular tie and the middle candidate gets eliminated.

Example:

40: A (the A voters truncate)
25: B (2nd choices of B voters aren't listed, since they're likely
       to be divided both ways, and we don't know which side would
       get more from them)
35: CB

***

The A truncation makes a circular tie, though B is the Condorcet
winner. In the resulting IRV count, B gets eliminated, and A
wins.

The reason why the A voters are in a position to make a circular
tie is because A beats B pairwise. Otherwise truncation or
order reversal would merely make C win. Since A beats B pairwise,
that means that A beats B in IRV after B is eliminated.

So pairwise, with circular ties solved by IRV is perfectly set
up to reward truncation & order-reversal, and to force a majority
to use defensive strategy to get its way.

The majority preferring B to A can only prevail if, when
A voters truncate, the C voters insincerely move B up to
1st place, with C. If A voters order-reverse, the only way
to keep A from winning is if the C voters actually vote B
over C, moving B to 1st place, and moving C down to 2nd place.

Of course the B voters could also thwart the truncation or
order-reversal, if they insincerely vote C over A. But, for
one thing, that requires that they know froml which side the
truncation or order-reversal will come.

I've just described the general pairwise defensive strategy.
With most pairwise methods, that's all that's available. With
Condorcet's method truncation isn't a problem, and order-reversal
can be thwarted by mere defensive truncation by B voters.



***

Mike Ossipoff
nkklrp at hotmail.com


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