[EM] General PR question (from Andy Jennings in 2011)
Toby Pereira
tdp201b at yahoo.co.uk
Fri Oct 3 04:04:06 PDT 2014
Kathy, would you be able to give some examples of this in action to flesh it out a bit? I'm a bit unsure about how it would work in practice. For example, if 1000 people vote for the candidates A, B, C, D, E and one person votes for A, B, C, D, F, then that one person is a very small faction. But If A, B, C, D are all elected then this very small faction (one person) has contributed to the election of four candidates, so I think it would cause your measure to rate it as quite unproportional. But in reality the one person is very closely related to the 1000 so shouldn't be seen as an entirely separate faction. We could also imagine a hypothetical case where although, broadly speaking, the voters are in factions, no two voters have identical ballots.
Toby
From: Kathy Dopp <kathy.dopp at gmail.com>
To: Kristofer Munsterhjelm <km_elmet at t-online.de>
Cc: Toby Pereira <tdp201b at yahoo.co.uk>; EM <election-methods at lists.electorama.com>
Sent: Thursday, 2 October 2014, 18:31
Subject: Re: [EM] General PR question (from Andy Jennings in 2011)
OK. Here's the formula that will *always* work to evaluate how
proportional fair any election result is, given any set of voter
groups and the combination of approval votes each group casts:
Sum(Absolute(v_i/v - s_i/s))
or
Sum(|v_i/v - s_i/s|)
Where v_i and s_i are, respectively the number of voters in group i
and the winning candidates group i voted for (for any group voting for
the same combination of voters)
and where v is the total number of voters and s is the total number of seats.
Thus, for an approval vote election, one fairly simple way to find the
most proportionately fair set of winning candidates would be to find
the set of candidates who minimize this sum of absolute values of the
differences between the proportion of the voters in each voting block
that votes for the same combination of candidates out of all voters,
and the proportion of seats that this group contributes to electing.
I am convinced this method of counting approval ballots will never
fail to assign the most proportional outcomes to select the winning
set of candidates. If there are more than one set of candidates with
the same minimum sum, perhaps toss a coin.
I actually like this proportional voting method very much because it
strictly adheres to finding the most proportionately fair set of
winning candidates, the vote tallies are easily precinct summable and
auditable, the vote casting method is easy and gives voters more
choice and flexibility to express themselves, and the method is fairly
(equally) counted for all voter groups. However, perhaps the summing
method with its proportions and differences in tallying the votes of
all voter groups voting for the same candidates is a little too
complex for some voters to comprehend.
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