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Technical discussion of election methods

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Two Lotteries

FS
Forest Simmons
Tue, Feb 23, 2021 9:34 PM

The first lottery is a proportional lottery:

From a randomly drawn ballot elect the lowest (worst) ranked alternative

that pairwise beats every alternative ranked ahead of it.

To trade in proportionalty for the Condorcet Criterion, complete the drawn
ballot with the help of additional randomly drawn ballots before finding
the alternative closest to the bottom that beats all of those closer to the
top.

The first lottery is a proportional lottery: >From a randomly drawn ballot elect the lowest (worst) ranked alternative that pairwise beats every alternative ranked ahead of it. To trade in proportionalty for the Condorcet Criterion, complete the drawn ballot with the help of additional randomly drawn ballots before finding the alternative closest to the bottom that beats all of those closer to the top.
FS
Forest Simmons
Tue, Feb 23, 2021 9:46 PM

Also the random solid coalition lottery ... draw ballots sequentially to
narrow down solid coalitions until only one candidate remains.

A solid coaliition is a subset of a ballot that is either the entire ballot
or what is left after truncating all of the candidates ranked below some
level.

On Tuesday, February 23, 2021, Forest Simmons fsimmons@pcc.edu wrote:

The first lottery is a proportional lottery:

From a randomly drawn ballot elect the lowest (worst) ranked alternative
that pairwise beats every alternative ranked ahead of it.

To trade in proportionalty for the Condorcet Criterion, complete the drawn
ballot with the help of additional randomly drawn ballots before finding
the alternative closest to the bottom that beats all of those closer to the
top.

Also the random solid coalition lottery ... draw ballots sequentially to narrow down solid coalitions until only one candidate remains. A solid coaliition is a subset of a ballot that is either the entire ballot or what is left after truncating all of the candidates ranked below some level. On Tuesday, February 23, 2021, Forest Simmons <fsimmons@pcc.edu> wrote: > The first lottery is a proportional lottery: > > From a randomly drawn ballot elect the lowest (worst) ranked alternative > that pairwise beats every alternative ranked ahead of it. > > To trade in proportionalty for the Condorcet Criterion, complete the drawn > ballot with the help of additional randomly drawn ballots before finding > the alternative closest to the bottom that beats all of those closer to the > top. >
KM
Kristofer Munsterhjelm
Tue, Feb 23, 2021 10:02 PM

On 23/02/2021 22.34, Forest Simmons wrote:

The first lottery is a proportional lottery:

From a randomly drawn ballot elect the lowest (worst) ranked alternative
that pairwise beats every alternative ranked ahead of it.

To trade in proportionalty for the Condorcet Criterion, complete the
drawn ballot with the help of additional randomly drawn ballots before
finding the alternative closest to the bottom that beats all of those
closer to the top.

How's proportionality defined in this context - of the method being a
proportional lottery?

-km

On 23/02/2021 22.34, Forest Simmons wrote: > The first lottery is a proportional lottery: > > From a randomly drawn ballot elect the lowest (worst) ranked alternative > that pairwise beats every alternative ranked ahead of it. > > To trade in proportionalty for the Condorcet Criterion, complete the > drawn ballot with the help of additional randomly drawn ballots before > finding the alternative closest to the bottom that beats all of those > closer to the top. How's proportionality defined in this context - of the method being a proportional lottery? -km