A simulation-based study of proximity between voting rules by Aubin, Gannaz, Rolland

A simulation-based study of proximity between voting rules by Aubin, Gannaz, Aubin, and Rolland (online HAL open science) has interesting working procedure.

but unfortunately it only looks at single-winner election systems.

goal is to to evaluate the utilitarian efficiency and strategy-proofness of these rules, and in so doing, group election systems into groups.

methodology using actual stimulations to assess similarity of voting systems

number of voters n =9,15, 21, 51, 101, 1001

alternatives [number of candidates] m =3, 4, 5, 6, 7, 9, 14

Distributions      Uniform, Beta(0.5, 0.5), Truncated Normal (0.5, 0.25, [.25?])

[I wonder how the vote allocation varies - too bad more information is not given, giving even one simulation in full detail)

surely uniform does not mean each candidate receives the same vote count!]

For each of the 6×7×3 = 126 combination of voters, alternatives and simulation processes, 1000 iterations have been run. [different vote allocations are not described]

A matrix of dissimilarity has been produced between the voting processes.

The distance between two voting rules is the proportion of situations where the two rules lead to the same winner.

Two voting rules are considered identical if their winner is always the same. The distance between them is then equal to 0.

Two voting rules are considered totally dissimilar if they always choose two different winners. The distance between them is then equal to 1.

Others distance scores should be possible (see below).

The obtained matrix for a given combination of voters, alternatives and simulation process is therefore a matrix of dissimilarity with scores between 0 (if two rules always agree on the same elected alternative) and 1 (if two rules always disagree on the elected alternative).

Therefore our study concerns 126 dissimilarity matrices. Therefore 126,000 simulations have been computed and combined to explore the influence of the number of voters, the number of alternatives or the evaluation simulation processes on the similarity of voting rules."

This is not an altogether useful experiment as it compares only single-member systems.

reference is made to

Tideman, N. (2023). Choosing among the variety of proposed voting reforms. Constitutional Political Economy, 34(3):471–481.

[also seems to address only single-winner election systems.

in "Proposals based on rankings" section, Tideman discussed whether ties of rankings should be allowed.

I agree, let ties stand and either give highest ranking to one of them, based on alphabetical ordering or based on popularity of the two candidates based on other voters' votes or based on some other criterion.]

Conitzer, V. and Sandholm, T. (2012). Common voting rules as maximum likelihood estimators. Proceedings of the 21st Conference on Uncertainty in Artificial Intelligence, UAI 2005.

[Like Aubin's study, this only looks at single-winner contests]

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so interesting concept as far as study of how election systems produce winners as measured by proportionality and percentage of effective votes.

But of course in final analysis, the District Magnitude is much more important than the method of election as long as the method is fair.

any system where winning candidate have same number, or about same number, of votes and where 80 to 90 percent of votes are used to actually elect someone will produce good party proportionality and fairness.

As long as multiple seats are involved in the contest, parties run multiple candidates, each voter has just one vote, there will be fairness.

whether some system as simple as SNTV is used, or elaborate as MMP, or any system where votes are used for candidate and for the party whose label he or she is running under, there will be much more fairness than under FPTP.

Both fairness and the percentage of effective votes increase if system allows votes to be pooled by party or to be transferred from an unelectable candidate to another with a better chance.

if a successful candidate has his or her surplus votes transferred, the fairness for large parties increases. But that party already has representation so it is not crucial for that kind of transfer to be done, if we only care about party representation - that most voters see someone of their preferred party elected.

But as the goals of elections are not only to see that each substantial party elects representation, but also to see that a stable government is elected (and it would be easier to get a governing party to approve of an electoral reform if it believes it can take a majority of seats if it comes close to a majority of votes),

we want to ensure that the PR system we propose will see that the largest parties get at least their due share of seats.

therefore vote transfer from successful candidates after they are elected is a selling point so that means STV.

Conversely, any system that uses levelling seats as top-up after districts seats are filled, where party vote shares are used to determine the party's due share of seats, in compensation for any disproportionality produced by district contests, would also address the governing party's desires.

unless governing party wants a majority of seats even if it takes less than a majority of votes - if that is the case (read Justin Trudeau (2017) here), then no PR system will be satisfactory to that party

Some countries have adopted PR when people drop out and stop voting or otherwise show dissatifactions with the voting system and how it wastes votes, (NZ)

others adopted PR when the social cost of electing an unpopular government is such that the risks of electoral reform are less than the potential for social disorder, riot, revolution, civil war. (Belgium, Switzerland,

The aspirations of a new country, as well as a new country's need to be inclusive, have pushed many new countries to adopt PR, instead of mimicking their former imperial power. (South Africa)

On the other hand, Canada has a backward election system.

This is actually a relatively recent situation.

Canada dropped its various alternative election systems and adopted universal single-winner FPTP in the 1960s (1990s in provincial elections), and has held to that warped system for the last decades, because

-Canadians are generally complacent and also generally well-served by their governments At least it could be worse - Canada has generally stayed out of conflicts, has respect for human rights (other than equal voting power, that is), public healthcare is great boon to general health and security, etc.)

-many voters are new and unwilling to rock the boat if older Canadians are satisfied.

-governments make mistakes but generally are non-intrusive.

-there are other places to go to in Canada if you don't like the provincial government where you are, or the city government where you are. Canada is big enough and wild enough to offer escape valves for dissatisfied voters.

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