# The big benefit of counting ballots cast, rather than votes cast, for "vote for multiple candidates" election results

Here’s a bloc FPTP election to make the point: suppose you have 3 candidates A, B, and C, and 3 voters. 2 of the 3 voters vote for A and B, and the third voter votes for C. Before even showing you the results, if A got 2 out of 3 voters to pick them, what % of votes would you expect them to get?
It turns out, they actually got 40%, not 67%! The reason is that most election results calculate a candidate’s vote percentage as votes cast for that candidate divided by votes cast for all candidates. So here, 2 votes for A + 2 votes for B + 1 vote for C = 5 votes for all candidates. The 2 votes A got are divided by the 5 votes for all candidates to be 40%. This problem applies to all “vote for one or more” elections, whether they have a limit on how many you can vote for or not.
The solution is to look at the number of total ballots cast in the election, not votes cast for all candidates. 3 people voted, so that’s 3 ballots cast in that election, and by dividing A’s 2 votes by those 3 ballots cast, we get the 67% reflection of support A deserved.
This is one more reason you can use in favor of a bloc Approval/Score (or even Approval/Score PR) ballot measure: even if a voter isn’t moved by Approval Voting itself, giving all candidates a more accurate reflection of support is something voters and candidates alike can agree on. This is actually a provision that made it into the Fargo ballot measure:

Reporting of results

For each candidate’s result in each race, reported vote percentages must be calculated by taking the number of votes for that candidate divided by the total ballots cast.

though not the St. Louis measure.

Rhetorically, it isn’t helpful to describe a ballot approving two candidates as casting two votes. People will claim that it is an admission that Approval violates one person one vote. However, I agree with your point. PAL election vote counts are often reported the other way, and it’s really annoying.

It is more important to consider the scores on each ballot which were used as votes. This is the amount of power the voter uses not what they express on the ballot. This should be the same for each voter to preserve the concept of one voter one vote. It is a sort of equity (equality of outcome) check. This is why I designed Vote Unitarity. It is the score implementation of Vote Equity. I think STV passes this since your vote remains whole and is passed around. I think MMP fails it as it is split into the partisan and member part which have different resultant powers depending on circumstances. Plurality passes in the trivial sense.

I would like this idea of Vote Equity to be adopted as a standard requirement along with Monotonicity, invulnerability to clones, ect

How is this relevant to the post? You may have meant to post this elsewhere.

There are three concepts:

1. Support given on Ballot
2. Ballots cast per Person
3. Support used to Elect

You are pointing out that it is important not to conflate the first two. I am pointing out that the third is likely more important than either and is truly what people mean by one person one vote. It is about preservation of vote power.

But this is more of an argument that Sequentially Subtracted Score or any Vote Equity system (which I imagine would always be PR-ish) are better than bloc Approval or Score. I agree, but that doesn’t take away from the point. In fact, even if you use a Vote Equity system with an Approval or Score ballot, you’d have to worry about the support of the candidates being artificially lowered again. Suppose two of the three voters in the top post’s example score A and B 10/10, and C gets a 10/10 from the third voter. You would need to make sure that it’s ballots cast that’s used in the results calculation, so that for A’s results the calculation is 20/10 = 2, then divided by 3, so that A has a “support level” of 67%. If it’s “total points scored/cast”, then that would drop it back to 40%.
Actually, this gets into interesting questions of how the results for a system like, say, Sequentially Subtracted Score would be reported. I imagine you’d report the score a candidate got at the point they were elected, so if a candidate had 200 points, then someone else got elected, and some points got shaved off the 200-point candidate’s voters’ ballots, and the 200-point candidate now had 150 points, you’d want to use 150 in the final calculation, not 200. So if there are 30 voters, maybe the now 150-point candidate is registered as having 50% of the votes, rather than the 67% they originally had.
The problem for the legitimacy of those results is that voters have no idea of the proportionality of any of the results just by looking at scores. With STV results, you know that each candidate gets elected with exactly a quota, but here, if someone got 50% of the vote in their PR election, what does that tell us about who they represent? It essentially separates the consensus-biased representatives from the more proportional ones on its own!

I do not think it matters if it is Bloc, single winner or multi-winner PR. The calculation might just be different. Bloc is equivalent to a few single winner elections. All single winner systems have vote equity. I think this means that the metric should be votes per single winner system. This divides through by the same number so you get the 67% result anyway. I think it is largely semantics.

As for sequentially Subtracted (Spent?) Score I would report both the overall utility across all ballots in addition the the score they were elected with in the round they were elected. It might also be useful to say how much they won by in that round. They for STV they show the ranking at each round. We could show score at each round. I see no issue.

I think the term “sequentially” is already quite advanced, subtracted just is too far. Perhaps just “Subtracted Score Voting” is fine; the point is not that it happens sequentially, but rather, that some points are subtracted when you elect someone. I think using “subtracted” rather than “spent” in this one is okay because it lends it just a hint of professionalism, similar to “transferable” in STV. But if you’re going with that word “sequentially”, I think “spent” is better.

The issue here is really, will voters feel a little short-changed or something if they notice their candidate was a consensus candidate, but someone else got their favorite. In other words, will they feel like a “sucker” when they could’ve gotten someone who’s a closer fit for them. Or, conversely, might they feel that “my candidate is part of the consensus majority, so they really have the most power. I feel bad for those ‘quota-only’ winners who will have no sway over the majority.” I suppose part of what makes consensus PR interesting is that multiple people “represent” you, so now I see why would want to analyze the spread/variance of utility, to ensure the scores don’t get divided up too much between various people. But on the other hand, it would be fascinating to see if people acquiesce to such divisions to ensure their representatives are part of the consensus majority, or so that they can slightly influence a member of that majority towards their viewpoint.

That is more of an argument for not using Monroe selection. If the winner at each round is the Utilitarian winner then people can’t really complain. If somebody has their vote whittled down by voters they scored 1s and 2s then maybe they will not be super stoked.

Isn’t it utilitarian selection that likely takes only a few points off your ballot at a time? After all, the first winner it elects is the compromise winner, whereas with Monroe, an actually proportional candidate can win the first seat on account of having more support in their Hare Quota. I believe we’ve gone over this before, but conceptually, it’s hard to believe.

In both selections an individual voter can have their vote power whittled down. In am not clear which is worse for it. I was more pointing out that it could be the case that the consensus winner does not win and that is a persons favorite. That seems wrong.

Now I have officially hijacked the post. I was really just trying to talk about the actual topic at hand.