Best counting methods?


It seems the concensus in Election Science is for Approval, Score, and STAR. Have I missed anything?

I am trying to create something to simulate as many counting methods as possible, hopefully with the same data: for example, changing all non zero Score votes to 1 would turn it into Approval.



We need simulations of multi-winner voting methods!!!

Here’s a page describing how to do it.

Here is the only multi-winner voting method simulation (it doesn’t test very many methods and assumes 100% honest voting)

Methods to test:

Harmonic Voting (score ballots)

Harmonic Voting (approval ballots)

PSI Voting (score ballots. The approval ballot version is equivalent to the approval ballot version of harmonic voting)

Monroe’s Method

Elbert’s Method

Sequential Proportional Approval Voting

Re-weighted Range Voting

Single Transferable Vote

Shulze STV


@Ciaran’s apportioned methods

As many of these other methods as possible


Doesn’t this thread fall under the Election Theory category?


And yet, the one proportional method that I actually take seriously is also the one proportional method that is impossible to simulate…

…or not?


It probably wouldn’t be impossible but it would certainly complicate things.


My career was a programmer or systems analyst and putting together web pages and scripts is a hobby only–no one is paying me and this is not part of a college project, degree program, dissertation, etc. I got into this when I was trying to learn how to vote against a FPTP leader a few years ago.
While I think my RCP and Condorset page is ready to fly (single & multiple winners) and I am ready to start something related to it, my time and interest in it are limited. What I am asking for are priorities. Assuming I can only work on a few of these before other demands on my time or (thus far unknown) health issues kick in, or I get hit by the proverbial Mac Truck (or worse, a real one), where should I start?


Start by deciding if you could potentially run a reasonably simple Asset election. If not, do Harmonic Voting (approval ballots), STV, and RRV.


There is actually a campaign @Sara_Wolf is putting together where we are going to come up with score methods which are proportional and then hopefully simulate them. We have narrowed in on sequential methods in multi-winner districts. RRV would be the most well known of these. @Jameson-Quinn has proposed an allocation implementation and I have proposed something as well which does unitary reweigting of score.


@Keith_Edmonds That’s awesome! Why haven’t I heard about this? Is there a forum that it is being discussed on?


I would say that the simplest (from the perspective of the electorate) system of score proportional voting is:

Add-On Multi-Winner Proportional Representation

It only requires an initial tiny bit of algebra.

You start by deciding the number of seats you need to fill:
T = The Total Number Of Tranches (i.e. (one less than) the number of seats to be filled).

The election is held and the votes are counted, and then every one will know the "strongest winner’s total (of votes), which we may call “W”.

Then any high school freshman can calculate the “bases of the tranches” (values of “B” corresponding to tranche numbers “N”) by simply plugging in “W”:

=/ B = W * ( 1 - [(N /( T + 1 )]^2 ) /=

Tranche #1 is the highest (just below the strongest winners position); tranche #2 is just below tranche #1, and so on.

This provides a party/interest-group blind method in which minorities of any sort can vote for their champions and have a reasonable chance of obtaining some degree of representation.

It will work easily with any kind of score voting.


It’s not proportional, nor monotonic. I don’t really see what this method has going for it. It looks like the method just penalizes candidates for getting scores that are too high, just for the sake of increasing randomness (which does not necessarily equate to proportionality).


Certainly add-on multi-winner proportional representation is proportional, since it causes some of the presumably “majority” candidates to give up some power to candidates that champion minority interests. That is precisely what proportional representation is.

As far as the monotonicity criterion is concerned, it seems likely that it cannot strictly apply to any system of proportional representation. And many other criteria that pertain to single-winner methods are most likely inapplicable to proportional representation methods. The idea that this method will be non-monotonic is obvious to the least well-informed voters.

As I said:
:~~~~~~~~~~~~~~~~~~~~ //
Down the thread a bit

From time to time “paladins” appear, who actually do good things for their constituents, and these paladins therefor get re-elected many times. But as described above, this tranche-proportional system would nearly always continually remove such paladins, and this is really disastrous. Something must be altered, so here is a solution. If any candidate who is an incumbent within a given tranche manages to receive enough votes to qualify as a potential winner within that tranche, except that there are potential winners who received more votes, That incumbent will displace (or “bump”) any non-incumbent winning candidates.
// ~~~~~~~~~~~~~~~~~~~~:

This would give minorities the ability to retain officials who were beneficial to their interests, and effectively remove any significant randomness.


If it were that simple, then just choosing 10 candidates at random would be proportional. But it’s not since if there are 50% Dem voters and 50% Rep voters, but only 1 Dem candidate and 99 Rep candidates, then no, the results are not likely going to be proportional. You can’t achieve proportionality by just punishing candidates for being popular.

Also, proportionality is a very restrictive property: it isn’t just an adjective you can add to any voting method that isn’t completely majoritarian. In order for a voting method to be proportional, it must have the fallowing property: whenever a group of voters gives max support to a set of candidates and does not give scores to any other candidates (or rank any other candidates higher if ranks are used), they are guaranteed to award to that set at least the number of seats that is proportional to the portion of the electorate that that group makes up (±1 seat).

If a voting method doesn’t have that property, it isn’t proportional. But it could still be considered semi-proportional, if at the very least it has this property: a hare quota of voters should be able to force the election of their preferred candidate regardless of how everyone else votes.

Don’t use the terms proportional and semi-proportional to describe voting methods that are not proportional nor semi-proportional.


Well yes! It really is that simple! And of course it’s not at all equivalent to choosing candidates at random.

Also you claimed:
=/ In order for a voting method to be proportional, it must have the fallowing property: whenever a group of voters gives max support to a set of candidates and… /=

Who gets to decide what the term “proportional” means? You? Wikipedia? Some dusty textbook? I do not think so. It is obvious that normal, ordinary voters would recognize add-on multi-winner proportional representation as being proportional. Perhaps you should argue with them.


Are you serious? About a voting method who’s only claim to “proportionality” is punishing candidates for being liked too much? I’m starting to think that nothing you post here is serious. That you are a troll. If this is true, find something better to do.


You are going much too far here. It should at least be obvious that I put a great deal of work into analyzing this method. Do you really think I go to the trouble of working through all this merely to annoy people such as yourself?

It is at least clear that this surprisingly simple method would provide a very reasonable form of proportional representation.

It is utterly impossible to provide some degree of power to minorities in the absence of some sacrifice of some degree of power by majorities. From some perspective this will necessarily have to give the appearance of “deprecating,” or even “punishing,” if you insist, the majorities.

You should also bear in mind that in the U.S. it is not possible to define minority group membership other than in a case-by-case manner. It is not even possible to create an absolute definition of gender. This is because the rights of freedom of speech and of association are strongly supported. For a time I happened to be the only white person who was allowed to attend Black Panther rallies in my community. Did that make me black even though I am white? Who knows? (They were actually split down the middle because half were Muslim and half were hippies. Those were distinctly different outlooks indeed.) Solidarity is an amazingly ephemeral phenomenon.

I am of the opinion that the interactions of human beings in the context of political elections, since people are sentient and can manipulate those election systems in unforeseeable ways, cannot be reliably simulated by means of computer programs. There are too many unknown variables. It may be worth doing, but it would be a serious mistake to ignore its limitations.

Do you think every one who does not think the way you do should be eliminated?

I would never write about add-on multi-winner proportional representation if I had not worked very hard to verify that it would be feasible. You should at least show some respect for that degree of effort.


Your method doesn’t make any sort of distinction what so ever between which voters are over represented and which are under represented.

You misunderstand the point of PR. In PR, electing candidates people do not like is not a goal. The goal, like in any voting method, is to elect people that voters do support. The difference is that in PR, the goal is to draw that support from all corners of the electorate by trying to make it so that more voters are represented by at least one candidate that they like.


You claimed:
=/ Your method doesn’t make any sort of distinction what so ever between which voters are over represented and which are under represented. /=

We cannot justifiably make such distinctions in an official manner. This is because it would entail the official recognition of specific parties. Only then could there exist some determination of how much representation they “deserve.” But this in turn would require the action of some authority to “recognize” such official parties. And that authority would naturally come to be co-opted by the existing most-powerful parties.

This takes us right back to square one, with “few-party” entrapment. This has destroyed all the democracies of Europe, which is now completely under the rule of the unelected European Union.


Not really. Every method I linked to above makes those distinctions without the official recognition of specific parties.

Example: sequential proportional approval voting.

Each round, the weight of each voters vote is equal to 1/(1 + how many candidates won so far that that voter approved of). The “how many candidates won so far that that voter approved of” part distinguishes between the voters that are over-represented and the voters that are under-represented.


European nations still have their own sovereignty. The EU can’t force European nations to do anything. They can only use trade deals as leverage to get their members to meet certain demands. If the EU did have sovereignty over European nations, then it would of been able to use that sovereignty to prevent the UK from leaving.

The EU parliament is the governing body that votes on European trade deals (what gives the EU the leverage needed to enact policy among EU members) and the EU parliament is elected by people who live in the EU.