[EM] Simulating multiwinner goodness

[Terry Bouricius]

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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