The Vacancy Solution to Exhausted Ballots

If we start with the assumption that all seats must be filled, we inevitably end up with the final seats being won too cheaply (e.g. on remainders), the price (as in RRV) or representativeness (as in Greedy Monroe) of a seat gradually decreasing, or the rate of load-unbalancing (in Phragmen) gradually increasing, due to exhausted ballots. This is unfair to exhausted surplus voters, who may not only outnumber unexhausted voters, but in fact may collectively have quotas, and would presumably prefer their quotas (or remainders, if the largest) to go to null candidates (i.e. keep the seats vacant), thereby increasing the power of the winners they supported. Asset voting is, of course, a better solution; however, because of transaction costs, it’s only a partial solution. I propose a vacancy solution, preferably in conjunction with asset voting (i.e. should seats exceed quotas after the trading window expires).

To be clear, I am not suggesting that seats should never be won on remainders. Rather, the remainder should have to be greater than the exhausted surplus vote divided by the number of remaining seats (I call this the Divided Exhausted Surplus, or DES quota). Or, at the very least, vacancy, treated as the candidate all exhausted ballots vote for, should be able to win seats like any other candidate. This version would be ideal for systems without quotas, like RRV or Phragmen. In STV, a voter should even be allowed to give “vacancy” an intermediate rank.

Are you trying to do this?

No, I’m trying to let vacancy be an option and effectively turn exhausted ballots (i.e. votes that still have weight but have nowhere left to put it) into votes for vacancy, as there’s no reason to suppose their casters would prefer them to be wasted and (if they’re represented) ample reason to suppose they’d prefer as many unfilled seats as possible to remain that way (rather than diluting the power of the winners they voted for). Perhaps a voter should be able to opt out of his final vote being for vacancy, but no rational voter would.

My DES Quota sequentially grows due to its numerator (exhausted ballots) sequentially growing and its denominator (remaining seats) sequentially shrinking. Its logic is that vacancies are maximized when the exhausted vote is evenly divided among as many null candidates as there are remaining seats. SSQ’s quota shrinks, of course, for a completely different reason (as you say, limiting free-riding), and does nothing to reduce wasted votes. The vacancy option could be applied to SSQ or any other system. Even the DES Quota could be applied to SSQ; it would be the limit to how small the sequentially shrinking quota could get, and there would be no seats won on remainders.

In fact, I think allowing voters to vote for vacancy is a quite moderate proposal. One could argue it doesn’t go far enough. One could argue we also need a fixed electoral threshold (a minimum number of voters a candidate ought to represent to earn his salary, benefits, floor time and complication of negotiation) that applies in the party-list case to all parties’ marginal seats. That’s debatable, but I don’t see how my proposal can be opposed by anyone who recognizes wasted votes or collective cloning (which is what wasting exhausted ballots incentivizes) as bad.

I understand what you are proposing I more meant the problem you are trying to solve. My point was that SSQ is supposed to solve the problem at the source. Your solution think it just makes things more complicated and it is not clear how to balance it properly so that you end up with each member of parliament being equal.

@Essenzia Has some ideas about just using a weighted parliament. I think this is his system

Other than your kind assurance, everything in your replies suggests I failed to communicate my solution. According to the Electowiki you cited (and presumably authored), SSQ is meant to solve SSS’s freeriding problem. My solution is a solution to exhausted ballots, not freeriding. In fact, SSQ’s shrinking quota results in more exhausted ballots, as being consumed by quotas is the only way exhausted ballots are removed in SSS and SSQ.

I don’t know what you mean. Each MP has one vote in parliament, so I’ll assume you mean equality in the sense of each MP representing the same number of voters, which is impossible. The vacancy solution does, however, increase balance, as the vacancies it would create by definition have more votes than the candidates that would otherwise fill them. Granted, vacancies do not represent their voters as well as the subset of winners those voters voted for, but vacancies are not unique in that regard; in any multiple or transferable vote system, you like some of the candidates you vote for more than others.

You won’t find a bigger supporter of weighted parliament than me. But weighted parliaments have unique problems. And while you and I don’t consider those problems significant, others evidently do, which is why you propose complex alternatives like SSQ, Essenzia proposes complex alternatives like DSV (which has nothing to with weighted parliament, according to the Electowiki you cited), and I propose simple alternatives like the vacancy solution.

Its relative simplicity cannot be denied. In the candidate version, you just add an additional candidate with the special property that electing him doesn’t remove him from the set of hopefuls. In the DES version, you just set an additional quota that is simply the number (i.e. the total weight) of exhausted ballots divided by the number of remaining seats.

First off, I can’t claim credit for SSQ. It was @Marylander’s idea I believe. Anyway, the problem you point out is the in sequential systems the cost paid by a group for their winner will be higher for the first few winners than for the last few. SSQ intends to do a readjustment at each round. Your systems would potentially not elect the last winner which would inflate the total influence of each elected so far. These are both getting at the same issue of each winner not representing an equal number of voters and as such the system is inequitable. The reason this is tied to free riding and vote management is that a large group can attempt to take advantage of this by electing two at a low cost at late rounds rather than 1 at a high cost in an early round.


This is the balance problem which SSQ attempts to solve too. It does so in a more continuous way than your idea so there will likely be less anomalies. Hard to say. I do not think either system is politically viable in the near future anyway so I am not inclined to put my efforts on this task. Glad you are.

I care much more about Prime Minister selection than voting on bills. Most weighted parliaments do not include a change in how that is done.

He edits those pages a lot and has several systems with similar names. Maybe @Essenzia could clarify which is the DSV like system which ends with a weight. Note that DSV is not proportional without a weight since there is no surplus handling.

I agree it is simpler but it may not have as much impact on the problem for the complexity cost. My actual preferred solution is to use a Vickrey Quota as outlined here

I disagree. SSQ is SSS-D’Hondt. Like other D’Hondt systems, the balancing effect of not letting seats be won for less than a half quota is opposed by the unbalancing effect of not letting seats be won for less than a full quota. D’Hondt is generally considered less proportional than LR (i.e. the unbalancing effect is understood to outweigh the balancing effect). Even if it weren’t, it would still increase the exhausted surplus rather than solve it, which is why proposing SSQ as an alternative to the vacancy solution is so odd.

I did a little research, and it turns out there are already vacancy candidates in the form of candidates who promise to leave any seats they win vacant. Remarkably, such candidates sometimes win (and make good on their promise), despite the fact that they require voters to make them their first choice, which my proposal would not do. The vacancy solution benefits those in power about as much as an unbiased proposal can, so there’s no obvious reason why it would be inviable.

I’m with you there, but shouldn’t it be assumed that the weights apply to PM-selection unless an explicit exception is made? The only polity I’m aware of that uses weighted voting for normal bills is the European Council, which uses the same weights for President-selection, just as corporations use the same weights for board-selection as they do for everything else.

As the shrinking quota’s impact is negative, so is its bang-for-complexity-buck. Moreover, the DES version of the vacancy solution actually reduces time complexity because the count and divide operation performed after each election is more than compensated for by the reduction in the number of elections.

I like the Vickrey Quota, just not your definition of it. You define it as the second highest tally, whereas the true Vickrey price (i.e. the second highest bid) is only as high as the second highest bankroll in a single-unit auction (even then, the equivalence only holds if bankrolls only have value in the context of the auction, but that’s a valid assumption in the case of voting) or the final round of a sequential auction. More generally, the Vickrey price is no greater than the average of the 2nd through (n+1)th (n being the number of remaining seats) highest tallies, which is never greater than Droop and is how I would define the Vickrey Quota.

To demonstrate the difference, consider the last South African election (South Africa is the only country I’m aware of that uses LR-Droop). If the actual national tallies were used to distribute seats in a single, national district, your version of the Vickrey Quota wouldn’t have changed a thing; the final seat’s cost would have been greater than the greatest savings from the Vickrey Quota. But my version would clearly have had an impact.

This is the mechanism SSQ is intending to use.

Perhaps, but the mechanism it actually uses is one that waits for the current quota to be unreachable, searches for the highest quota reachable if applied retroactively, and then applies it retroactively. That’s much more complex and and more advantageous to large parties than the Vickrey Quota as I’ve defined it.