[Election-Methods] Measuring satisfaction in a multi winner election

[Stéphane Rouillon]

Hi bunch,

this mail oriented me toward a nother subject I like:
Measuring satisfaction among voters.

When comparing the result to the possible candidates, one
can determine its level of satisfaction by the proportion of
candidates elected compared to the number that received
support form the voter.

In FPTP,  each voter is either fully satisfied or fully unsatisfied.
Hence the global satisfaction rate is the average of the ballot
fraction received by each elected member.

With a multi-seat method, the same technic can be applied for each specific
group of voters who agree on the same elected members, counting
a fraction of satisfaction proportional to the ratio of elected/wanted 
representativ.
For example, with 3 available seats and ten candidates (A to J), let's 
analyse
the global satisfaction:

45% of voters : A > B > C > J> ...
5% of voters: B > C > A > J > E > ...
30% of voters: G > H > I > A > C > J > ...
20% of voters: J > A > B > ...
Outcome A, B and C elected.
(this is a typical STV outcome)

Thus the first 50% (45%+5%) are fully satisfied: 100%
The 30% are not satisfied: 0%
The 20% got 2 elected representative among their 3 first candidates: 
66.6% of satisfaction.
Global satisfaction: 50% x 100% + 20% x 66.6% = 63.3%

Using another method (approbation with the cut-off at ... for example):
Outcome A (100%), J (100%), C(80%).
Establishing satisfaction at this point is more complex I admit.
Some will argue that with approbation philosophy 100% satisfaction is 
reached
when the 3 elected are among the approved candidates. Ranking partisans will
argue that the preference ordering still exist and only the first 3 
preference should be considered
for a fair comparison between systems.
I am an in-betweener: sometimes we don't  have the detail of the 
preferences (a real approval ballot does not give
this information) but on the other way approving 10 person and having my 
8th, 9th and 10th picks elected would not fully
satisfy me. Thus I split equally satisfaction among each apporved 
candidates: 4 approved candidates => 25% satisfaction each.
The average reflects my understanding of the measurement.

Satisfaction of the 45% group: 75%
Satisfaction of the 5% group: 60%
Satisfaction of the 30% group: 50%
Satisfaction of the 20% group: 66.6%
Global satisfaction: 45% x 75% + 5% x 60% + 30% x 50% + 20% x 66.6% = 65.1%

The best electoral system should maximize global satisfaction.
In this particular example: Approval gives a better result than STV.
I invite you to measure satisfaction with your preferred multi-winner 
method.
SPPA (my favorite) produces high satisfaction levels.

Stéphane

Kevin Venzke a écrit :
> Hi,
>
> --- Howard Swerdfeger <electorama.com at howard.swerdfeger.com> a écrit :
>   
>> but most of these reforms fail to recognize that that Seats do not equal 
>> power. So we are still still stuck with a similar problem (votes !=
>> power)
>>
>> I was looking into 2 methods of measuring power in a weighted voting
>> system.
>>
>> http://en.wikipedia.org/wiki/Banzhaf_Power_Index
>> http://en.wikipedia.org/wiki/Shapley-Shubik_power_index
>>
>> I was wondering first if there are any methods of measuring power in a 
>> legislature that I am unaware of? Secondly if anybody has tried to 
>> design a generic system where by votes are kept proportional to power, 
>> via allocation of seats?
>>     
>
> I find this question very interesting... But I am guessing that you don't
> have many allocation possibilities, especially with a small number of 
> factions.
>
> Another thing: I guess it wouldn't be cloneproof. Say there's normally
> only three parties and everybody votes for a party list. I guess a
> party could gain an advantage by running two lists instead of one.
>
> Kevin Venzke
>
>
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