# [EM] Simulating multiwinner goodness

Terry Bouricius terryb at burlingtontelecom.net
Thu Mar 11 06:42:21 PST 2010

```Brian,

But obviously, real world satisfaction with an election outcome is not so
straight forward. I may favor a certain slate of candidates, but feel huge
dissatisfaction if they all win, such that there is no opposition in the
legislative body to "keep them honest." This is what happened for many in
British Columbia in 2001, when the Liberal Party won 77 out of 79 seats in
the Provincial legislature.

The utility, or hoped for happiness measurement before the election may be
changed BY the election results themselves. While this is especially true
of multi-seat elections, it is even true of single seat elections. I may
want my candidate to win, but be disappointed if she wins despite the fact
that a majority of voters preferred another candidate (due to a feature of
the voting method)...My preference for majority rule may trump my
candidate preference.

Terry Bouricius

----- Original Message -----
From: "Brian Olson" <bql at bolson.org>
To: "Election Methods Mailing List" <election-methods at electorama.com>
Sent: Thursday, March 11, 2010 7:35 AM
Subject: [EM] Simulating multiwinner goodness

There was a question on the list a while ago, and skimming to catch up I
didn't see a resolution, about what the right way to measure multiwinner
result goodness is.

Here's a simple way to do it in simulator:
Each voter has a preference [0.0 ... 1.0] for each candidate. Measuring
the desirability of a winning set of candidates is simply summing up those
preferences, but capping each voter at a maximum of 1.0 satisfaction.

Unfortunately, this won't show proportionality. If 3/4 of the population
have a 1.0 preference for a slate of 3/4 of the choices, we would measure
electing one of them as being just as good as electing the whole set.

So, we could apply the quota. If a candidate is elected by 3 times the
quota, only apply 1/3 of each voter's preference for that candidate to
their happiness sum.

Now the huge coalition with their slate elected should each add up to
about 1.0 happiness, and smaller coalitions should get theirs too.

This is sounding a bit like an election method definition, and I expect
that this definition of 'what is a good result' does pretty much imply a
method of election. At worst, given ratings ballots that we can treat as
the simulator preferences, for not too large a set of winning sets of
candidates, get a fast computer and run all the combinatoric possibilities
and elect the set with the highest measured sum happiness.

Another thing we could measure in multiwinner elections (and possibly
single winner) is the Gini inequality measure. If we have a result with
both pretty high average happiness and low inequality, that's a good
result.
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