## Asset voting – an interesting and very simple multiwinner voting system

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.

Inventors: Several people invented versions of this system independently, each thinking they were the first inventor. The first inventor I am currently aware of was Lewis Carroll in 1884, but it then was pretty much forgotten for 85 years. It then was invented by me (Warren D. Smith) and independently by Forest Simmons. Smith invented the name "Asset voting" which seems the best name so we'll stay with it.

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:
• In Simmons' version: just the name of a single candidate.
• In Smith's version: 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. Simmons' version is the same as Smith's provided only vectors of the form (0,0,0,1,0,0) are permitted (a single 1 for the selected candidate, all other entries 0).
• In Carroll's version: an integer C-vector each entry of which is nonnegative and with all the entries summing to some fixed pre-specified integer. For example a legal vote could be (7, 0, 3, 2) in a 4-candidate election, if the pre-specified sum were 12.
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 drop out in increasing order of "wealth", 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. But I prefer unrestricted negotiations and instead assuring termination by simply declaring a pre-specified deadline "all negotiations end at midnight November 7." S.J.Brams suggested the refinement that in addition to some fixed deadline at midnight after (say) 5 days, there also be intermediate deadlines each prior midnight; if the winner-set has not changed since the last one then the negotiations end (early) then. And it would be beneficial to have some kind of publicly-readable bulletin board announcing at all times the current status, i.e. how much assets each candidate currently owns, and the terms of any inter-candidate deals.

Note that Forest Simmons's variant is the simplest for the voter, since they can use Plurality-style ("name one candidate") ballots (the named candidate gets 100% of that voter's assets).

You could also compromise between Smith's 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 is exactly Carroll's version (here with prespecified sum "3").

### 2. Example

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

#Voters their vote
38 Bush
37 Gore
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).

### 3. Possible extension to have "Weighted Congressmen"

An optional possible extension of asset voting which could yield even finer proportionality still, is this. The W winners (now "congressmen") can be made unequal in the parliament. Instead, they each will have a "voting weight" proportional to the asset-count that elected them. For example, we could imagine having equipopulous districts, each of which elects three (not one) members of parliament; and then after those three MPs are elected with (say) 37, 31, and 26% of the assets, we rescale to 39.36, 32.98, 27.66 so the sum is 100%, and these become their respective voting weights in parliament.

Disadvantages of weighted congressmen: More complicated. Need computerized voting system inside parliament (most already have one). Should they be paid unequally and have unequal staff?

1. If every voter were matched up with "her personal representative" in parliament, who agreed with her on all issues, and if the MPs each had voting weight equal to the number of "their" voters, then the resulting representative government would be optimal in the sense that

For every binary decision, the parliament's weighted vote would yield the same result as would have been got by a simple majority vote of the entire voter population.

This is the ideal of proportional representation. Asset voting with weighted congressmen seems to come closer to meeting that ideal than all or almost all rival PR systems (including plain asset voting), and does so very simply.

2. With random-seeming weights, tied votes in congress would essentially never happen anymore.

3. The chemist Dave Robinson, and the University of Wisconsin math professor Anatole Beck, and economics and law professor Gordon Tullock (1922- ; this was in ch.10 of his book Towards a mathematics of Politics, Univ. of Michigan Press, Ann Arbor 1967), all independently invented a PR scheme that Robinson called direct representation (DR), albeit I think a better name might be "weighted congressmen." (But DR does have the advantage that it coincides with Dave Robinson's initials.) Robinson, tracking it back through history, found that similar proposals had been invented already in the USA in the 1860s by Joshua Francis Fisher (1807-1873, author of The degradation of our representative system and its reform, C.Sherman Son & Co. Philadelphia 1863, and Reform in our municipal elections, Kildare, Philadelphia 1866), and Simon Sterne (1839-1901, author of On representative government and personal representation, J.B.Lippincott & Co. Philadelphia 1871). Robinson set up a web site http://www.directrep.org to promote his idea.

In their scheme, everybody votes for their congressman using plain plurality voting, but then all candidates win, not just the one with the most votes – but they obtain voting weight in the parliament equal to their number of votes. This scheme again sought to approximate the ideal of "proportional representation," and also you as a voter would nearly always have a representative to approach who'd be interested in fighting for what you want, and who tended to be sympatico with you.

Although that goal is laudable and this plan initially sounds simple – when you think about it, several annoying issues crop up, which have to be dealt with in ugly ways:

1. Since "everybody wins," a huge number of people, say 101, might want to run, which would make life difficult for the voters, and also yield an enormous parliament. That would be ridiculous.
2. We could cure that problem by, e.g. only allowing those with at least 26% of the vote (or some such threshold) to win... but that would not work because then zero people might win!
3. OK, trying again, we could instead insist on having exactly min(3,C) winners if C candidates run (the three with the most votes). I'm using "three" for concreteness while explaining, but have no special attachment to that particular value. But that would destroy the perfect representation ideal, for example with C=101 and the top three getting a few percent each, 90% of the voters would be left "unrepresented," a huge failure of the sought-for "all are represented" ideal! Plus plurality-voting pathologies like "vote splitting" then would rise out of their coffins like vampires to damage democracy.
4. OK, trying yet again, we could also demand that C≤10, i.e. at most 10 are allowed to run, in an effort to limit that kind of damage. But then: who would be the favored 10 allowed to run, versus the 91 not allowed to run? They would have to be selected using some unfair process, or perhaps by a fairer one such an an extra preliminary election using, say, RRV. That would, at the very least, ruin the simplicity of the scheme.
5. Perhaps with DR congress would contain a lot of "extremists" who (since they only need to please "their own" voters) would not compromise ⇒ gridlock.

At this point the reader should be seeing the virtues of our alternate plan of just using asset voting with weights=assets! It implements "DR without the ugly kludges":

1. There is no problem if a huge number of candidates want to run and no need for a preliminary election (or some unfair process) to winnow the field – the asset voting process itself takes care of that.
2. No thresholds are needed.
3. It is no problem to make the number of winners be min(C,3).
4. Plurality voting problems like "vote splitting" no longer arise and the "finer representation" and "asset transfer" properties of asset voting mean that everybody is represented – unlike those who voted for non-winners in the Tullock plurality-voting scheme being left unrepresented with no ability to affect the election outcome.
5. Asset-voting's "negotiation" stage would tend to select for those willing to compromise (i.e with proven negotiation ability). If polarized gridlock congress would be a risk with original-plan DR, that risk might now be reduced or avoided.

Possible Census suggestion by F.Simmons: For USA use, the exact count by the Census of the district population, could be used when weighting congressmen by assets, thus further ironing out inequalities.

### 4. 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; albeit this round-to-integers defect is removed with the "weighted congressmen" variant).

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

1. this simple and
2. proportional.

Indeed, arguably nothing else even comes close. And if you want a system that

1. can be used on "dumb" voting machines,
2. is "proportional," and
3. involves voting for people (not "voting for parties" which is what "party list" PR systems instead involve)

then again, Asset arguably has zero competition.

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.)

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.

Note: the discussions of many of the below criticisms of asset voting have now been heavily revised in view of points made by Gabe Bodeen in 2013, who pointed out some criticisms of the criticisms that everybody (including asset-inventors Simmons and Smith) had managed not to notice for years. Bodeen's points largely or entirely refute the criticisms. Hence asset voting is now looking a lot better even than its inventors Smith and Simmons had realized.

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 feel 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 example by Raphfrk aimed at demonstrating 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.

But in 2013, Gabe Bodeen criticized that criticism. Bodeen argues that it is probably wrong to believe that Centrist will give his assets to one of the extremists. That prediction was based on the view that Centrist, as the asset-poorest, would think "I have no chance to win, so I might as well serve as kingmaker during negotiation-stage."

Bodeen's negotiation hypothesis: Bodeen instead thinks that the candidate who will give up his assets to serve as kingmaker will be the one under the most political pressure to do so. Other wordings: "with the most to lose" or "with the most at stake." That, he contends, is how concessions in negotiations really work!

And in Raphfrk's scenario, Bodeen predicts that "blinks first" candidate will be Leftist, who hence will act as kingmaker to enthrone Centrist. This, happily, will be the best choice for society, voiding Raphfrk's criticism. Why?

• Centrist (if truly a centrist) will (if he's motivated by idealism) see little political advantage to preferring Leftist over Rightist (or vice versa). And if he's instead motivated by political pressure: the trouble is that Centrist will experience pressures to swing the election one way or the other, but those pressures are in both directions and will largely cancel themselves out.
• Meanwhile, Leftist experiences a lot of pressure that is mostly 1-way, i.e. not 2-way and hence cancelling out. His supporters are screaming at him: "if you just sit there, the hated Rightist will win, the worst possible event. Since you are going to lose anyway, why not save us from that fate by enthroning Centrist?" Centrist voters (who are not his direct supporters but still important possible future friends/supporters) also want him to give it to Centrist.
• Finally Rightist is under no pressure. His supporters are saying "Hang onto your assets; you will win unless the evil rivals make a deal, but there is nothing you can do about that except try to urge Centrist to give you even more. You can also urge Centrist to Hold Firm, but then if Leftist enthrones him, you have no reason to, and if not, then you just win."
• Centrist's supporters will recognize the above and urge Centrist to hold firm, forcing the higher-pressured Leftist to give him the Gold. To the extent Centrist feels unlikely to win, that also works to relieve the pressure on him. Might as well just sit there and hope for victory.

I currently suspect Bodeen is right, or anyway more right than alternative hypotheses, in which case Raphfrk's criticism is refuted.

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

Here is a second "Asset is bad" example by Bruce R. Gilson for 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 (as a voter) 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.

Note that Gilson unhappily feels some incentive to vote dishonestly in such an asset election, i.e. not to give his assets to his true favorite A.

Multiwinner escape hatch: 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.

But again, Gabe Bodeen criticized Gilson's whole criticism and without need of the multiwinner escape hatch. Again, Bodeen argues that the first person to pay during negotiations is going to be the one "with the most to lose," not the one "poorest in assets" or "with the least chance to win." In Gilson's scenario, A is not under a lot of uni-directed pressure. The pressures on her partially cancel out. But again, whoever among {B,C} is not leading (say B), would be under a lot of uni-directed pressure to improve the situation by enthroning A, who is not as bad (from the perspective of B and B's supporters) as C. So Bodeen predicts that in this situation B would "blink first" and hence A would win the election. And hence Gilson was best off voting honestly for A.

So again, to the extent Bodeen is right, this criticism is refuted.

Corruption? The asset system might encourage corruption in which the candidates misuse their power as elected officials (once they win, or if they already are in office running for re-election) to pay off rivals for their "assets" using real public assets, such as "a million dollars." Actually practically every voting system encourages cheating and corruption; the fear with asset is that somehow perhaps the corruption-incentive is greater and hence the problems will be greater. I find it very hard to quantify whether and how much that fear is true.

Another comment by Stephen Unger: 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.

Response to Unger by William Waugh: Voters could simply cast vector-votes assigning any nonnegative numbers to the candidates. (Failure to mention a candidate counts as assigning zero to him.) Then each such vector-vote could be automatically "normalized" (by dividing each number by that voter's total sum). The voter then would not have to compute the sum nor worry about making sure it was right, since this automatically would be done for her.

Waugh also suggests: Assigning zero to all candidates could be regarded as a "vote of no confidence" in the candidate list. If a majority of the voters do that, then we could redo the nominations, campaign, and election.

A rather different response to Unger by Curmudgeon: I like the idea of discarding votes like (0.3, 0.5, 0, 0.4, 0) which fail to meet the sum-constraint. Serves as a mild intelligence-test or preparedness-test for voters, thus enriching the electorate in smarter, more prepared, or more competent voters.