Asset voting – an interesting and very simple multiwinner voting system

(Executive summary)   (Return to main range voting page)

Asset voting is an "unconventional" voting system in which both the voters and the candidates participate. (Warning: this bothers a lot of people, and also it prevents asset voting from being used at all in abstract scenarios with candidates that are not people, such as voting to choose pizza flavors.) It's designed for situations where several (not just one) "winner" is to be selected from a field of candidates.

It was invented by Warren D. Smith, and also a very similar system was invented independently by Forest Simmons, much to their mutual surprise I would imagine (if I were them. Which, actually, I am.) To our even-greater surprise, it turns out to have been invented by Lewis Carroll in 1884, then forgotten for 85 years!

Asset voting has been proven to be (in terms of certain criteria) superior to any "conventional" system, see paper #91 here. How does it work?

Asset voting to elect W winners from C candidates, 0 < W < C:

  1. In a C-candidate asset election, each vote is a real C-vector (i.e list of C numbers), each entry of which is nonnegative and with all the entries summing to 1. For example a legal vote would be (0.4, 0.3, 0, 0.3) in a 4-candidate election, since 0.4+0.3+0+0.3=1.
  2. Compute the sum-vector S, that is, the list of each of the C candidates' totals.
  3. Now regard each Sn as the amount of an "asset" now owned by candidate n. The candidates now negotiate; any subset of them may redistribute their assets among themselves.
  4. After all negotiations and redistributions end, the W "wealthiest" candidates win.

In variants, only certain kinds of redistributions are permitted, for example the candidates in increasing order of "wealth" drop out, redistributing their assets among the remaining ones as they do so. This "poorest first" variant has the advantage that it forces the procedure to end quickly and everybody knows when it has ended.

Forest Simmons recommends that electorates that don't want to deal with any ballots other than Plurality style ballots, should use a simpler version of Asset Voting that uses only Plurality-style ("name one candidate") ballots (the named candidate gets 100% of that voter's assets).
You could also compromise between the above and Simmons' approach by, e.g, providing the voter with three plurality-style ballots, enabling her to split up her vote three ways – or fewer by using more than one of her three ballots to vote for the same candidate. This "compromise" approach was Carroll's version.

Example

In this example, we suppose for maximum simplicity (or because we are using Simmons's variant) that each voter votes for just one candidate.

#Voters their vote
38 Bush
37 Gore
20 Nader
5 Buchanan

This is a make-believe analogue of the 2000 US presidential election. It's unrealistic in several ways, the most obvious being that it was a one-winner election, not a multiwinner election (asset voting can be used for single-winner elections but is intended for more-than-one-winner elections). Ignore the unreality. We are just trying to illustrate how it might work in a simple and familiar way.

In this election, Nader could decide to drop out of the picture and award his 20 asset points to Gore. (Both Bush and Gore would, no doubt, try to make deals with Nader to try to get his assets. But, let us suppose that Nader, after considering his options, the offered deals, and the fact he considered his views closer to Gore's than to Bush's, preferred Gore.) In that case, Gore would win with 37+20=57 asset points to Bush's 38. (Buchanan could also decide to give his assets to some candidate, but in the particular scenario here, Buchanan's decision would not be able to change the winner.)

Now if this were a 2-winner election, then both Bush and Gore would be winners no matter what Nader and Buchanan decided to do (albeit either Bush or Gore could in theory cause either Nader or Buchanan to be a winner by sacrificing their own chances – not likely).

What is good about Asset voting?

It is extremely simple – especially Simmons's variant. The Simmons-variant works on every voting machine in the USA, including noncomputerized ones, right now, with no reprogramming and no modifications required. And it can be "counted in precincts," i.e. a sensible notion of "subtotals" exists (unlike for some rival voting systems such as STV).

Asset is proportional. That is, if 40% of the voters are "red," 35% are "blue," and the remaining 25% are "green," then – provided candidates always award their assets to other candidates of their same color-type – the result of the election will be 40% red, 30% blue, and 25% green winners (up to perturbations caused by the requirement to round to integer numbers of winners of each type; with 20 winners these percentages will be exact, but if there are 19 winners then exactness is not achievable).

That's usually considered better than disproportional systems in which, e.g. 51% red voters versus 49% green ones, will yield 100% red winners and 0% green winners. In contrast, e.g. the "cumulative" voting system can yield highly disproportional results in which, say, 51% "red" voters elect only a single red winner, while meanwhile the 49% green voters elect 9 green winners.

There is no other voting system in the world, which is simultaneously (a) this simple and (b) proportional.

Asset is "monotonic," i.e. giving more of your vote to candidate X can help, but not hurt, X (at least insofar as we are talking about the prenegotiation stage of asset voting). Some other systems like STV disobey that.

Asset is "participatory," i.e. voting honestly is never worse for you than not voting at all (again, at least insofar as we are talking about the prenegotiation stage of asset voting). Some other systems like STV disobey that.

Asset is "fair" in the sense it treats all candidates equally, regardless of their membership (or lack thereof) in political parties. (Some other systems like "party list voting" are not at all fair in that sense.)

Asset has considerable immunity to "strategic voting," i.e. it tends to be in your best interests as a voter to vote honestly. For example, in the fake-2000 election above, voters who voted for Nader or Buchanan were not "wasting their votes," since they expected Nader or Buchanan to use their votes the way that voter would herself have wanted to use them if Nader or Buchanan were not in the race. So it was not strategically foolish to vote Nader or Buchanan even if those candidates could not win. Indeed, (a) Nader might win, so it is foolish for Nader-favoring voters not to vote for him, (b) Nader, even without winning, could gain negotiating leverage and hence possible deals from Gore and Bush (e.g. a cabinet seat, policy concessions), in which case Nader votes would be generating genuine power. In this sense Asset delivers a finer degree of proportionality than any conventional voting system – even candidates with too few votes to win a seat still often get some power.

In contrast, e.g, with cumulative voting any vote for a candidate with no chance to win is simply wasted. Such votes are strategically stupid even if that candidate is your true favorite, giving you the voter a distressing choice between being a "fool" and being a "liar," and also causing small political parties to get smaller and die over time, leading to fewer choices for voters and a worse democracy. With asset voting, you are much less likely to be forced into such a "Sophie's Choice."

With asset it is easy to allow "weighted voting" where some voters have more votes than others.

Asset may tend to encourage inter-candidate cooperation and reduce "negative advertising" and bullshit aspersions (since you might need to make a deal with candidate X, it does not pay to alienate her!). Also it may reduce legislative "gridlock" since those in congress would consist (to a greater extent) of those with proven negotiating capability, and also legislators could depend on each other in future to be elected (whereas right now, they have no electoral incentive whatever to cooperate). Warning: this paragraph, although it may be entirely true, is also speculative; i.e. it is supported by some intuition, but not by actual evidence.

What's bad about Asset Voting?

Some people are bothered by the fact that "deals" could decide an Asset election. On the other hand, other people consider that good. For example, if you vote for Snodgrass, presumably it is because you want Snodgrass to have power. Why are you then complaining if Snodgrass then exercises that power to try to alter policy, get cabinet post, etc? Wasn't that your goal? And if Snodgrass uses his assets differently than you expected (yikes!) then presumably Snodgrass, if he had been elected, would have acted differently than you expected too. In that case, again, we don't see why you are complaining – it's your own fault for misjudging your candidate. Not the fault of Asset Voting – your fault. Voter misjudgements happen. (But presumably you as a voter are less likely to make a misjudgement about a candidate if it is your favorite candidate, than if it is somebody you do not actually like or trust, but feel forced by an unfair voting system like plurality to vote for anyhow.)

Warren Smith (one of the asset voting inventors) suspects that the worries about "deal making" with Asset Voting will be more serious if it were used as a single-winner voting system (which is not recommended – Smith only recommends for multiwinner elections) and hopefully less serious and/or less common in multiwinner scenarios. But this suspicion is not currently supported by any solid evidence. Here is an bad example by raphfrk of Asset Voting dealmaking misbehavior in a single-winner scenario.

#Voters their vote
38 Rightist
25 Centrist
37 Leftist

In this situation, had we been using a more conventional good-quality voting system such as range voting or a Condorcet system, quite likely Centrist would have won, because the Left and Right voters would each prefer the Centrist over the Other Side. But with Asset Voting, it is highly unlikely the Leftist and Rightist will place the common good over their personal careers and power, hence one of them (whichever one the Centrist prefers) will win the election. That's an example of a plausible scenario in which the Asset Voting result would presumably be less good for society. IRV also would malfunction in this situation by refusing to elect Centrist.

Asset might tend to encourage lock-step party-loyalty. Or it might not. Hard to tell.

Here is a second bad example by Bruce R. Gilson of asset voting used for single-winner elections, inspired by the 2009 NY district-23 congress race:

Suppose the following situation. There are three candidates, A, B. and C, and two salient issues, X and Y, for simplicity. Suppose I agree with A on both issues X and Y, I agree with B on issue X but not Y, and I agree with C on Y but not X.

Also, suppose I consider X much more important than Y, but A considers Y more important than X.

I would best be represented by A (who agrees with me on both issues) in a legislature; A would vote "my way" on both. She (I'm thinking of Scozzafava in NY-23, that's why the feminine pronoun!) might not be as enthusiastic when X comes up for a vote as I would be, but she'd vote my way on both, so she'd represent me best.

However, if A found herself to be an untenable candidate, she would cede her votes to C – who would be the worst choice from my point of view (exactly what Scozzafava did in that election, by dropping out and endorsing Owens). She considers Y (on which she agrees with C) more important than X (on which she agrees with B). So in an asset-voting situation, she'd delegate her votes to C.

I'm not saying Scozzafava was, in fact, perfect from my point of view – I'm sure there are a lot of issues that divide us. I'm talking about an idealized situation, and while I think of A as Scozzafava, B as Hoffman, and C as Owens, I don't know the candidates well enough to be certain they really fit. But somewhere, in some election, this situation would crop up. Range voting would work better in this kind of situation.

Both raphrk's and Gilson's problems vanish (or at least "diminish" or "become less frequent") if asset is used only for multiwinner elections, which since they involve more winners also involve more candidates, and hence there is more chance there is some candidate (or several) closely resembling you. I suspect asset misbehavior-examples like these are only common when it is a single-winner election (or maybe also 2-winner) but uncommon if 3 or more winners.

Stephen Unger comments: I see one serious problem with Asset Voting. Asking voters to cast vector votes that sum to some fixed amount is asking too much. I doubt if more than three out of four votes would be valid! The simpler Simmons idea of just one vote per voter of course avoids this.

The reason we cannot just have a more-simple ordinary range-style vote, without the sum constraint, is this. That could lead to highly disproportional results. E.g. there are 5 Democratic clones running versus 1 Republican. 37% of the voters vote (1,1,1,1,1,0). The other 63% vote (0,0,0,0,0,1). Then the Democrats, highly unfairly, win by a landslide! So it is essential to have the sum constraint which causes "assets" to be conserved and fungible rather like "money," so that we get proportionality. (A lot of naive multiwinner voting-system designs can lead to highly disproportional results, this asset-misdesign is just one example of that.)

Why would we want to use the more-complicated sum-idea as opposed to Simmons's simpler voting style? Well, perhaps we would not (since simplicity is important)! But there can be reasons to prefer vector-style voting over Simmons's simpler approach, if simplicity is not a concern; we know of several scenarios where it appears to help. How common or important such scenarios are, is not known.


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