# Consensus on IRV & Runoff?

Forest Simmons fsimmons at pcc.edu
Wed Jan 30 10:43:05 PST 2002

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On Wed, 30 Jan 2002, MIKE OSSIPOFF wrote:

>
> With Runoff, if the sincere CW comes in 1st or 2nd as indicated
> favorite in the primary, s/he can't lose.
>

This suggests another method that satisfies the Condorcet Criterion:

The method gives the win to the CW if there is one.  Otherwise, the
against the method winner restricted to those ballots that did not give C1
first place support.

Note the recursive form of the definition.

In practice it would be very likely that the ballots not giving first
place support to C1 would have a CW even if the full set did not, so the
following computationally tractable truncation of the method would be a
good approximation to the full method:

Give the win to the CW if there is one, otherwise the candidate C1 with
the greatest first place support goes head-to-head against the CW of those
ballots that did not give first place support to C1, unless this
restricted ballot set has no CW, in which case the candidate with the
greatest first place support among the restricted ballot set (i.e. the
candidate with second greatest first place support in the full ballot set)
is the contender against C1.

In other words, if neither the full ballot set nor the restricted ballot
set has a CW, then the (truncated) method reverts to ordinary two step
plurality runoff.

The non-truncated method is the only method fully consistent with the
assumptions that (1) the CW should be the winner if there is one, (2)  if
there is no CW, then the candidate C1 with greatest first place support
should be one of the finalists in a runoff, and (3) the voters that do not
support the first finalist C1 have the right to determine who the other
finalist is.

Forest

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