It has been pointed out to me that a simple, perhaps unacceptable and dumb, approach to integrating approval votes into a global whole for multiple seats that holds that each ballot approving N possible candidates/parties can be simply divided by N, so that if someone approves 3 options, their vote appears as 1/3,1/3,1/3 for each choice they made, and so on, is in fact the same thing as Cumulative Voting, and I observe that FairVote’s description in fact identifies this precise format of it, where a voter simply marks their approved choices, is described as “Equal and Even” Cumulative Voting.
Now @AssetVotingAdvocacy and others have suggested that we might much prefer to let each voter shift their approval to be more for one choice than another, as we would accomplish if say it were a score ballot, so if there are 3 total levels, including zero, with 2=Strongly Approve and 1=Moderately Approve, voting SA for one and MA for another ought to route 2/3 of one’s vote to one and 1/3 to the other. Indeed that might work fine, and it seems as amenable at this early stage of my thinking to a straightforward quasi-proportional computation of global shares of seats for a multimember body. The question I hope to shake down is, will this approach, in simplistic Approval binary form or more elaborate Score form, indeed produce something voters will recognize as a fair proportional distribution, or will it tend to have perverse and unacceptable distortions of fundamental voter intent? Running made-up scenarios where I know the minds of the categories of voters, I can compare outcomes to single-choice “prime” votes where the voter must simply choose one as in conventional list proportional systems, and thus see if the voters are likely to accept the variations assuming they informally think they know the electorate’s general pattern of prime preferences, or just have reason to like or dislike the outcomes, and judge whether they are being fair or not in any complaints they may have. But if we run a real world election without a parallel poll of prime preferences, we probably cannot infer the mental state of the voters from the cardinal polling data–and if we do have a single choice prime poll in parallel, we might as well just use that for proportional outcomes, unless we find the processing of cardinal votes has advantages voters might come to value in this application as well as in settling single seat races.
So I begin with Approval only, possibly with some Asset voting cleanup of the last seats, to see what is what and if we hit big snags. I suppose that if we can map Score voting into fractional index points within a hypercube and do all manipulations straighforwardly from that that we can with the binary vertices of an Approval combination index hypercube, then perhaps extending the method to Score might fix problems, or perhaps just make them worse, so let’s run and find out!
Now, the basic approach for Approval being to discount each ballot’s individual score by dividing by the total number of approved choices (this is separate from using the same ballot without any discounting in settling a district race it might have been cast in) most of the complex high-dimensional manipulations we would value a symmetrical, regular frame like a hypercube for will not apply really. I pointed out in my little essay on N-cube generation referenced above, that in general, we can turn an N-cube onto its axis between the zero vertex, where all voters who left the ballot blank are recorded (if we care) and the opposite “omega vertex” where all choices are marked approved above it, and the result is tiers of combinations possible, beginning with a first level of N bullet vote combinations where N is the number of candidates and hence N-cube dimensions, so for a plain 3-cube this is three points, and for a 2-cube aka square where we have just 2 candidates of course this is 2 points. Just below the single Omega vertex at the “top” we will have the same number of all-but-one negative bullet votes, anyone but the one omitted that is, and as we add total choices marked going up or subtract them going down, we will have mirrored numbers of combinations of 2 out of N = number of combinations of N-2 out of N, etc until they meet where half the choices are marked and half not. Each of these levels of the hypercube polarized this way corresponds to x out of N possible votes cast, and thus per Equal and Even Cumlative voting, when we note how many ballots match a given combination, we just divide them by x, the number of choices used.
But we don’t need to visualize hypercubes for that, we can just count positive binary digits marked in a simple binary representation of each combination!
Asking people to visualize the N-cube is mainly me fishing for math-minded people seeing ways of handling the cube on a higher level for quick direct outcomes. But simply noting each combination and discounting it according to its number of choices used, and then adding up the discounted ballots cast for each party, should total up to the number of ballots cast, and give us a simple if fractional real number score for each party that we can then run through a standard proportionality formula to crank out seat shares for each party.
So this is simply doing a Cumulative Vote, and the question here is, what might be wrong with that approach?
I should point out there is extensive material on CV because it is widely used by corporations to elect Board of Directors and so forth, and there it is not used generally in a one person one vote application, but rather in a one-share, or one-dollar, one vote way. Shareholders with more investment weigh more in the outcome. CV is generally recommended as the option that small shareholders would prefer the company use to maximize their chance of getting some direct representation on the Board. That strikes me as a big win given my concern for what I call “positive representation.” But of course any aspects of practical business world use of CV involving relationships between bigger and smaller shareholders would be irrelevant, in democratic government we have one person one vote–everyone is an equal “shareholder.”
Ideologically it need not be that way of course, plenty of people think it can and should be otherwise, with some people counting more than others in public affairs. The commonest form is binary–some people should be allowed to vote, they say, others should not at all. But I think anyone adhering to the idea for any adult person is in fact abandoning any advocacy of democracy as such, in favor of some kind of aristocracy, and by a slippery slope is liable to take it straight to plain dictatorship. So here assume it is in fact equal votes cast by all, with any discounting resulting from a person spreading their favor around, the total of it adding up still to one vote overall.
Looking now at Wikipedia, I don’t find the article exactly comprehensive, lacking as many Wikipedia articles on a voting method have, a deliminated pro versus con section.
I do gather from it two issues in the corporate world are
In a corporate setting, challengers of cumulative voting argue that the board of directors gets divided and this hurts the company’s long term profit.
Clearly this translates in the political sphere to general objections to PR in favor of the two-party “Duveger’s Law” as a counsel of virtue–that it is broadly and deeply a good thing for voters to be forced to choose one of two partisan camps in order to be effective, as each of these big tent parties will compel diverse factions to agree on a common plan of action. I think most though perhaps not all of us here reject this conventional wisdom, although CES’s culture of smiling on moderate compromise candidates as unfortunate victims of “center squeeze” and other maladies bothers me as a turn in this general direction. Meanwhile a corporation is a profit-making machine, and stipulating they should or anyway do exist as such, the values for it are not those of governing a human society at large. Also, I would venture the humble opinion I would certainly side with the small shareholders if I were in a position to be a shareholder at all! Perhaps as a Rawlsian exercise I should consider my point of view were I instead a very very large shareholder, but I think the general principles telling me diversity in governance, as well as checks on the strong by the allied not so strong, are generically good things from which benefits arise offsetting any difficulty in one strong hand steering the whole decisively–or like as not, on hasty impulse!
Here is a different category of issue–the general principle that the smaller the number of seats up for election at one time is, the less fine grained any representative system is, so that larger numbers are needed to make minimal impact on the body. This is true of any representative system whatsoever and is not a special issue of cumulative voting therefore.
Farther down in the article, we come to
Voters in a cumulative election can employ different strategies for allocating their vote.
See also: Tactical voting
We have here people who denounce any hint of strategy in voting as a sign of something rotten. Certainly I value transparency and rewarding straight up honest evaluation of candidates–one reason why I am skeptical about the importance of multiple options in voting if we can guarantee global proportionality in total body makeup; pick your favorite and back them, is the value I think predominates and ought to. Tactical voting should not emerge ideally. But realistically, all voting has some aspect of strategy to it, because all bodies should integrate all the electorate in all its diversity, and inherently there are conflicts of interest and need to build effective alliances, which will be in conflict at least on specific issues. Let’s see how daunting the issues are.
It is important to bear in mind also, that in most CV systems, such as that proposed by Lani Guinier, the candidates do not appear, save as noted as a point of information, as party delegates, but as individuals, and so much of the discussion of strategy relates to voters having to judge which candidates to support and how widely or narrowly to spread their votes, and picking just one of several can waste votes by overspending them on one when there were ample votes to elect several–vice versa if there are not enough votes to do that, spreading them can dissipate the votes and waste them that way.
However, if a vote for a person is also a vote for their party, or if votes go directly to parties with party lists, I think this aspect is corrected automatically; overconcentration on one party candidate will transfer excess votes to the others via elevating the share of the ticket as a whole, and spreading votes within a party’s nominees will concentrate them on the one getting the most even if that share by itself is not enough to elect one. The votes transfer where needed via party affiliation in the version I envision therefore.
Allotting more than one vote to the same candidate, or plumping , can make that individual more likely to win. …
Conversely, spreading out votes can increase the number of like-minded candidates who eventually take office.
With parties, which I have noted can be defined and organized for electoral purposes in a way that is open to individual candidates and minimally organized ad hoc candidate compacts, both spreading overconcentrated votes and consolidating over-scattered ones, I think the voters can concentrate on backing the one they want most and let the process sort out which win directly and which owe their victories in part to also rans, with either party organization or simple moral debt serving to get some degree of representation for most everyone fairly.
The strategy of voters should be to balance how strong their preferences for individual candidates are against how close those candidates will be to the number of votes needed to win. Consequently, it is beneficial for voters to have good information about the relative support levels of various candidates, such as through opinion polling.
Such information is always helpful, if one can learn how many grains of salt to take it with, to any voter in any electoral system. I think the inclusion of options of party alliance largely relieve the voter of needing to strategize much beyond choosing whom and what they like best.
Voters typically award most, if not all, of their votes to their most preferred candidate[ citation needed ].
So there we have it, in reality, at least in electoral systems in government with one person one equal share of choices, we get mostly bullet voting, which does not bother me! I will perhaps be exaggerating rather than underestimating the degree of spread out multiple choices in upcoming thought experiment examples.
Turing to the other survey I have found, FairVote’s description, let us see if there are more conundrums to consider there–but first here is another corporate focused page’s considerations:
Problems With Cumulative Voting
Cumulative voting can also be a negative thing. Using this voting method makes it easy for disruptive single candidates to get on the board of directors. This kind of voting system also makes it almost impossible to remove a director once elected. A small section of shareholders can block the move, even if most of the voters approve.
Again we have the caution against diversity, in the form of the fact that one person’s bold advocate is another’s counterproductive and obstructionist hothead. This is in the nature of true positive representation; if people some consider bad and troublesome exist in society, then per John Adam’s “mirror in miniature” prescription for the Legislature of a democratic republic, they will be present in the body too.
Similarly, positive representation means that many though not all representatives of a faction will be impossible to get rid of. Each self-defined interest group “mirrored” in the body will, as long as their program remains coherent and relevant, have a core of supporters who stick to it thick and thin, again as long as their representatives remain faithful to them as they judge it. Under positive representation, if this faction has a quota of the electorate, they can keep reelecting this core cadre in proportion to their core numbers, indefinitely. Again bearing in mind surely some of these perennial delegates would surely be painful and deplorable from say my point of view, it is of the nature of the project of positive representation they are there to stay–unless events evolve so as to render their base of support mobile and shifting to other configurations they cannot or fail to adapt to. It is in the power of the voters who sent them there to either keep or remove them–this is much of the point! Corporate governance, even if we suppose these warnings dire in the for-profit world, is not the same thing as social governance.
Now on to FairVote’s perspective:
CV, however, has its drawbacks. One is the problem of a like-minded constituency splitting its vote. For example, if a voting constituency or a political party has too many candidates, it can “split” its votes among its own competing candidates and not win a fair share of seats. Candidates also must compete aggressively against candidates in their party – such intra-party competition can undercut coherent parties. In order to prevent vote splitting and intra-party competition, a party or like-minded constituency often seeks to limit candidacies and organize individual voters to allocate their ballots among those candidates. As a result, some argue that CV can concentrate too much power in the hands of leaders of parties or non-partisan communities of interest.
That pretty much repeats what Wikipedia said more laconically, but the extra discussion gives better insight. Again party organization is an answer, and as I conceive the system working there is no need to strategically rein in the number of candidates anticipating a limited number of votes that need to be concentrated; whatever share of votes the candidates get will automatically be conserved proportionally. The matter of inter-candidate rivalry on a party slate is something new to consider. One way to deal with this if it becomes problematic is to revert to party lists and have voters vote for parties alone, but I think that generally speaking it should just be left to politics; if voters observe candidates in so-called party unity or alliance bickering in response to their own (that is the voters’) judgement as to who gets what level of support, they can judge which of them are most suitable and which not politic enough to be supported in future. With the open ended party formation mechanism I outlined, where a group of independents can ad hoc form a compact, one purpose of making the rule one of unanimous mutual consent was precisely to flexibly and simply lay the problem of sorting out differences and strategy among themselves; if they cannot work with one another according to declared principles of unity, they should split! And then voters choose which fragment they like better-- or turn to a third group showing better organization! Vice versa a party can bootstrap itself into being via unanimous adoption of a charter, and the included bylaws can have procedures agreed to by the partisans to regulate these circumstances. The default rule remains that within a party share, the candidates who got the most votes (or equivalent, scores, in a cardinal system) fill the seats, so indeed the candidates are competing with each other in a sense. Managing that is part of their campaign strategy; the voter can rely on choosing the one they like and seeing where the dust settles.
Most everything else FairVote has to say about CV seems entirely positive.
My takeaway is that providing for votes to individual candidates to double as votes for their party, bearing in mind a very open and flexible way of effectively forming coherent parties (that is, as coherent as this faction and the voter support they seek to attract want it to be!) takes care of the most serious conundrums.
Now it remains to be seen–if we have an electorate where the little man behind the curtain, me and others here interested in simulations, know what the traditionally defined proportional balance of parties would be, and we assume an election by Approval Vote is held by these voters who cast AV obscuring their prime choices as I define them, will the outcome, with a substantial number of voters voting other than bullet votes, resemble the voter intentions, or diverge in unfortunate or perverse ways from it?
If CV works well enough, then probably it can generalize pretty simply to Score voting–say we call that “Equal and Directed Cumulative Voting,” meaning that instead of dividing by the number of candidates chosen, we divide by the sum of the scores in each ballot, then multiply by each score, so a voter voting two party/candidates a 9 each on a scale of 9 is counted as voting 0.5 to each, but another voter voting 9 to one and 6 to the other is counted as voting 0.6 to one and 0.4 to the other, and a third voter voting 9 to 5 options is counted voting 0.2 to each. Each voter adds up to 1 and is thus equal, but has the power to shift their single vote among several as they like, or of course to simply bullet vote.
Note this means that if a voter votes only one candidate any positive score, and that score is a lousy 3 out of 9, they are not very happy with anyone, but still count as a full bullet vote for the one they gave a grudging low score to. I think this is fair; in a single choice system they would face the same conundrum if they were such curmudgeons as to acerbically despise every single option on the ballot! They can stay home, of course, or on this line item refuse to mark anyone. What they ought to do, of course, is prior to the election urge some candidate they would like to run, then bullet vote a 9 for this brave soul. If they don’t campaign and this person has no wider net of appeal, the vote is essentially wasted of course, because this lonely candidate will not have much of a score overall nor any large share of the body! But a certain number of such voters are inevitable, it is impossible without direct democracy to satisfy every voter, and even then those outvoted are going to lose on policy anyway. A final asset vote for subquota share seats might give an outlier with serious effort and non-joke candidacy some important weight in enabling a more popular candidate to clear the bar to representation, and so it should be worthwhile even for the hardest to please to set up candidates that do merit their full approval, even if hardly anyone else thinks they do. Failing this effort, a sullen single low rating still signals which of the available choices the tough to please voter thinks is least bad, and that counts for something, especially since they could just refrain from voting at all.
So I don’t think we need to discount low maximum score combinations; as by instead dividing each combined score sum for x number of choices by x times the maximum score. We divide by total combined score sum period, for one person one vote, and consider that open nomination, and positive representation, and possible further frugality with votes via asset voting, all say that each category of voter should be able to be pleased by someone and it is not the rest of the electorate’s fault if they are not, so some least bad candidate might as well benefit from inflated support.
Bear in mind, the curmudgeon and/or Eeyore voter, whether that way out of spite or gloom, is effective in their low scoring in any district races with single winners, where their low score only slightly benefits the least bad option grudgingly chosen; it is only in figuring a global score derived outcome that their ballot gets turned into Polyanna against the voter’s will.
But I need to see some exercises before gaining confidence CV is really good enough–if it is that is one possible and probably becoming my favorite way to get meaningful proportionality or something like it from cardinal votes. And I need to compare, for a given set of existing votes, what other recommended processes such as Thiele or alternatives here developed arrive at instead; if their results seem to tend to be superior, it will be necessary to turn to math to see if there is a direct way other than iterative to get their outcomes, and take entirely different approaches than just normalizing cardinal votes as outlined here; such an alternative would not be CV at all.