by Michael Ossipoff
In my Democracy Chronicles articles, I have variously advocated Approval, Score, ICT, Woodall, Benham, and IRV. The reason for the different recommendations is that I was recommending for different kinds of conditions. First let me define four kinds of voting conditions:

First Voting Condition: Current Conditions

These are the conditions that we have in the United States in 2014. Disinformational, agenda-promoting, media, and an electorate who believe those media, at least on the matter of party-winnability and regarding the matter of what other people prefer. The public believe the media’s constant message that the Democrats and the Republicans are “The Two Choices”.

Given the media’s constantly-repeated claim that only a Democrat or a Republican can ever win, progressive voters, under current conditions, feel strategically-compelled to bury their favorite in order to help the Democrat. Therefore, under current conditions, we need a voting system that never gives any favorite burial incentive, no matter what media-caused misperceptions voters have. In previous articles, I’ve defined the Favorite-Burial Criterion (FBC):

A ballot top-votes a candidate if it doesn’t vote anyone over hir, and it votes hir over someone. A candidate is at top on a ballot if that ballot top-votes hir. For elections in which there is only one winner (i.e. when there are no ties). If the winning candidate is a candidate who is top-voted on a certain ballot, then moving an additional candidate to top on that ballot shouldn’t result in the winner being a candidate who isn’t now top-voted on that ballot. The result is that you can fully help a compromise, while still top-voting your favorite.

For current conditions, we need a voting-system that meets FBC. Otherwise, our election-results will continue to be quite meaningless, as voters continue to abandon their favorites in order to help a “lesser-evil”.

Second Voting Condition: Voting systems for Current-Conditions

Approval, Score (also called Range, and the Point System), Improved-Condorcet-Top (ICT) (defined in previous articles), and Symmetrical ICT (SICT) are voting systems that are workable as a fix to current voting conditions. Of these systems, ICT has the further advantage of not being subject to the chicken dilemma, but Approval has the briefest definition and is the minimal change from Plurality.

My earlier articles at Democracy Chronicles emphasized Approval and Score, because I was advocating for current conditions. But the fact is that voting-system reform, or any reform, is very unlikely under current conditions. It later occurred to me that by far the most likely way for voting-system reform, or any reform, to happen, will be by first electing a better political party to office, using our existing Plurality voting system. Hence my current emphasis on what I call the Green scenario, and the voting systems that would be optimal under Green scenario conditions.

Third Voting Condition: The Green Scenario

Suppose that a progressive political party were elected to office, and formed a government such as offered in that party’s platform. The party could be any progressive party, such as a non-socialist progressive party (GPUS Greens, Justice Party, Pirate Party, etc.), or a democratic socialist party (G/GPUSA Greens, or SPUSA), or any of the communist parties.

The media would no longer be disinformational, and, anyway, any electorate who could elect a progressive party under current conditions would have to be an electorate who could no longer be successfully deceived by disinformational media. Therefore, in voting, favorite-burial induced by media disinformation would no longer be a problem, and FBC would no longer be needed. That would make possible another desirable combination of properties: The Mutual Majority Criterion (MMC), and the Chicken Dilemma Criterion (CD). That combination of properties is incompatible with FBC, but is available when we no longer need FBC.

I defined MMC, and described the chicken dilemma, in my earlier article, _Voting Systems for the Green Scenario_. The Chicken Dilemma Criterion (CD) is intended as a precise measure of a voting-system’s freedom from chicken dilemma. CD is defined at electowiki, but I’ll copy its definition here:

The Chicken Dilemma Criterion could be summed up as “1-sided coalitions don’t count.” The A voters are the voters who vote A over everyone else. The B voters are the voters who vote B over everyone else. The C voters are the voters who vote C over everyone else.

1. There are 3 candidates: A, B, and C.
2. The A voters and the B voters, combined, add up to more than half of the voters in the election.
3. The A voters are more numerous than the B voters. The C voters are more numerous than the A voters, and more numerous than the B voters.
4. The A voters vote B over C. The B voters refuse to vote A over anyone.
5. None of the C voters vote A or B over the other.

Requirement: B doesn’t win.

In the chicken dilemma scenario, described in the premise of the Chicken Dilemma Criterion, (CD), defined above, if B won, then the B voters would have successfully taken advantage of the A voters’ cooperativeness. The A voters wanted to vote both A and B over the candidate disliked by both the A voters and B voters. Thereby they helped {A,B} against the worse candidate. But, with methods that fail CD, the message is “You help, you lose”. Some methods do pass the Chicken Dilemma Criterion including ICT, Symmetrical ICT, MMPO, MDDTR, IRV, Benham’s method, and Woodall’s method.

Because CD is such a simple situation, could there be another simple implementation of it? Maybe one that doesn’t speak of numbers of voters in the factions?

Though CD is sufficient, as-is, here is a non-numerical definition of it:

The A voters are the voters who vote A over everyone else. The B voters are the voters who vote B over everyone else. The C voters are the voters who vote C over everyone else.

1. There are 3 candidates: A, B, and C.
2. If the A voters and B voters all voted both A and B over C, then C couldn’t win.
3. The ballot set is such that if C withdrew from the election and the count, A would win.
4. The A voters vote B over C.
5. The B voters don’t vote A over anyone.

Requirement:B doesn’t win.

That combination of properties, MMC and CD, is compatible with the Condorcet Criterion (CC):

1. “X is socially preferred to Y” means that the number of voters who prefer X to Y is greater than the number of voters who prefer Y to X.
2. If there’s a candidate who is socially preferred to each one of the other candidates, and if everyone votes sincerely, then that candidate should win.

IRV (defined in previous articles, including “Voting Systems for the Green Scenario”) meets MMC and CD. Benham’s method and Woodall’s method (defined, along with IRV, in the _Voting-Systems for the Green Scenario_ article) meet MMC, CD, and CC. Though IRV, Benham, and Woodall have already been defined, in the “Voting-Systems for the Green Scenario” article, their brief definitions should be included here as well:

IRV:

A candidate tops a ranking if s/he (not necessarily alone) has no one currently voted over hir in that ranking, but is voted over someone, by that ranking. Determine which candidate tops fewest rankings. Delete hir from all of the rankings. Repeat till only one candidate remains un-deleted. Elect hir.

and…

Benham’s method:

1. “X beats Y” means that the number of ballots ranking X over Y is greater than the number of ballots ranking Y over X.
2. Do IRV till there is one un-deleted candidate who beats each one of the other un-deleted candidates. Elect hir.

Of course if, initially, before any IRV is done, there is already a candidate who beats each one of the others, then, b the above definition, that candidate wins, without any IRV being done. That is likewise the case with Woodall’s method, defined below:

Woodall’s method:

1. The Smith set is the smallest set of candidates such that every candidate in the set beats every candidate outside the set.
2. Do IRV till only one member of the initial Smith set remains un-deleted. Elect hir.

As before, of course if initially, before any IRV is done, there is one candidate who beats each one of the others, then the Smith set consists only of hir. As the only member of the Smith set, then, by the above definition, s/he is immediately elected, without doing any IRV. CD is important, because, when there’s a chicken dilemma,  a mutual majority can lose because of rivalry and distrust among its members. Five U.S. political parties, four of them progressive, offer IRV in their platforms:

• G/GPUSA (original U.S. Greens, socialist Greens)
• GPUS (currently largest U.S. Green party, non-socialist)
• SPUSA (Socialist Party USA)
• Peace & Freedom Party (mostly in California, socialist)
• Reform Party

Since IRV is the only non-Plurality voting system offered in a party platform, that means that we have a good head-start toward the next voting system being IRV, a method that meets MMC and CD, and therefore is a good method for the Green scenario. Of course Benham and Woodall would be better still, because in addition to MMC and CD, they meet CC. Benham is only a minimal change from IRV and therefore is probably the most likely improvement on IRV, if people realize that it would be better to additionally meet CC.

Fourth Voting Condition: Ideal Majoritarian Conditions

What if the electorate were no longer susceptible to chicken dilemma? Maybe someday similar political parties won’t feel rivalry among each other. Then, without a need to avoid chicken dilemma, we could choose a voting-system entirely on the basis of its majoritarian performance under sincere voting.  For instance, there are a few majority-rule criteria that are incompatible with CD. One such is SDSC:

Strong Defensive Strategy Criterion (SDSC):

If a majority prefer X to Y, then  they should have a way of voting that will ensure that Y can’t win, without any member of that majority voting someone s/he likes less equal to or over someone s/he likes more (other than when not voting either over anyone).

While CD says “1-sided coalitions don’t count”, SDSC says that 1-sided coalitions do count, and can keep a majority-disliked candidate from winning. Hence, CD and SDSC are mutually incompatible. Therefore, if we are sure that the electorate are not susceptible to chicken dilemma, then it would be desirable to use a voting-system that meets SDSC.

When neither FBC nor CD is needed, but majoritarian-ness is still desired, then we have ideal majoritarian conditions. Then, our choice of a voting-system can be based entirely on how well the voting-system does, by majoritarian criteria, such as CC, MMC, SDSC, and maybe others. Ideal majoritarian conditions are certainly farther off than Green scenario conditions. It’s well that the voting-system offered in party platforms is one (IRV) that’s good for the Green scenario, because Green scenario conditions will be the next ones that will obtain, if we’re able to make any progress (by electing a progressive party to office).

After this article, my next one will be “Methods for Ideal Majoritarian Conditions”. So, in this article, I don’t say much about such methods (Ideal majoritarian methods). I’ll just define one such method, the one that I consider the best one, Ranked Pairs (RP). RP has several versions, which deal differently with equal defeats or pairwise-ties (two things that can happen when there are very few voters, as can be the case in polls, families, committees, organizations, etc.). Here is the basic RP definition, one that disregards those few-voters conditions, though it’s usable under those conditions too.

Ranked-Pairs (RP):

1. A “defeat is an instance of one candidate beating another (as defined above in this article).
2. A “cycle” is a cyclical sequence of defeats, such as A beats B beats C beats A.
3. A defeat “contradicts” a set of other defeats if it is in a cycle consisting of only it and them.
4. If X beats Y, then the strength of that defeat is measured by the number of people who rank X over Y.
5. A defeat is a discarded defeat if it contradicts a set of not-discarded defeats that are stronger than it is.
6. The winner is the candidate who doesn’t have any not-discarded defeats.

That defines RP when there are no equal defeats, where defeat strength is defined as above. But, in organizational elections or family elections, or in polls, with fewer voters, there can be defeats that are equal in strength, making it desirable to add to the above definition, to take equal-defeats into account.

The above RP definition can be, and sometimes is, used for counting RP even when there are very few voters. But, its disadvantage for such small elections is that, when there are equal defeats or pairwise-ties,  it can discard insufficiently many defeats, sometimes failing to return a winner, resulting in unnecessary indecisiveness or vulnerability to clone-candidates.

The best RP version for small elections is MAM, defined below. It uses randomization to deal with equal defeats and pairwise-ties. There are other RP versions, without randomization, that avoid the problem of not discarding enough defeats—but they can discard _too many_ defeats, again resulting in the same problems.

Maximize Affirmed Majorities

For family, committee, organization or poll elections, the following changes could, and, for best results, should, be added to the above-stated basic RP definition, making a different version of RP, known as Maximize Affirmed Majorities (MAM):

Add the following to #4 from the Ranked Pairs definition above:

But, if the number of ballots ranking X over Y, and the number of ballots ranking A over B, are equal, then the XY defeat is stronger than the AB defeat if the number of ballots ranking Y over X is less than the number of ballots ranking B over A.

If there are equal defeats in a cycle together, and they’re equally weakest in the cycle, or if they’re the only defeats in the cycle, then you must randomly choose one of the ballots in the election. That randomly-chosen ballot is used to determine which of those equal defeats is higher in the “dominance-order”. In any particular election, only one random ballot is chosen, and it is used to determine dominance-order wherever needed in the count.

As for the particulars of how the randomly-chosen ballot determines the dominance-order, for that I refer you to Steve Eppley’s MAM website. You can find it by searching “MAM, Steve Eppley” at google. I’ll cover that detail in my next article, “Voting-Systems for Ideal Majoritarian Conditions”. Therefore, in MAM, the above definition of a discarded defeat, statement #5, is changed to:

5. A defeat, D, is a discarded defeat if it contradicts a set of not-discarded defeats, each of which is either stronger than D, or equal to D and above it in the dominance-order.

The dominance-order effectively makes it as if there were no equal defeats. When there are few voters, the advantage of MAM is that it doesn’t discard unnecessarily many defeats.  That’s desirable, because a defeat is a public decision that a certain candidate (the defeated one) shouldn’t be elected. But MAM also doesn’t indecisively leave unnecessarily-many defeats un-discarded. Thereby, it avoids the above-named problems of non-randomizing RP versions.

Based on some numerical attributes of the set of rankings, maybe with some arithmetic operations being done on certain numbers describing the rankings-set,  a pre-announced rule chooses one of the rankings as the basis of the dominance-order for that poll or election.

There are various  RP versions that don’t use randomization. One of those will be described in _Voting-Systems for Ideal Majoritarian Conditions_. But, when there are few voters, those non-randomizing (“deterministic”) RP versions suffer from the above-described disadvantages, when they discard unnecessarily many, or indecisively-few, defeats.

Another ideal majoritarian method is called “Beatpath”, or “Schulze’s method”. But, in simulations by Steve Eppley and Norman Petry, it was found that, in the vast majority of instances where Beatpath and MAM choose differently, more voters prefer the MAM result to the Beatpath result than vice-versa. The Condorcet Internet Voting Service offers four rank-counts, by which to automatically count polls at that website:

• Benham (referred to there as Condorcet-IRV)
• MAM
• Basic RP, as defined above (referred to there as CIVS-RP)
• Beatpath (referred to there as Schulze)

There’s convincing evidence that successful chicken dilemma defection isn’t happening in polls, and that, therefore, polls aren’t having any chicken-dilemma problem. So, evidently, the conditions that obtain in polls are ideal majoritarian conditions. Therefore, for polls, such as those at CIVS, I recommend MAM. That best of all ideal majoritarian voting systems is one of those that is offered at CIVS, for automatically counting its polls.

BONUS: Non-Majoritarian, Unselfish, Sincere-Rating Conditions

Suppose that, in some particular electorate, maybe a family, organization, group of friends, or committee, voting is as described immediately-above, in this section’s bold-face section-title. Instead of wanting to get the best result for _themselves_ that they can get, they’re instead only interested in fairly getting the result that, by some measure, best maximizes the _overall_ group happiness with the result. Such voters would rate sincerely, in the ordinary points-rating system, which is sometimes referred to as “Score”, “Range”, “the Points System”, or sometimes “Cardinal Ratings”. That voting system, Score, would be a good choice for the conditions referred to in this section.

But there’s a caveat to that: Even if the electorate are unselfish, that doesn’t mean that these point-systems would be the best choice. Maybe voters are so altruistic that they would falsify their ratings in order to benefit other member(s) of the family or organization. For that reason, I consider the ideal majoritarian methods to usually be a more reliable choice for family and organizational voting. Additionally, voting is easier and simpler by MAM’s rankings, than by Score’s ratings.

But I feel that there’s still a circumstance that could justify Score: Suppose there are very few voters, and that you want the best decisiveness, without need for randomization. Score, with a wide range of available scores, such as 0 to 100, or -100 to 100, might be the easiest way to achieve that.

But, in a hypothetical, far-in-the-future, society, in which the electorate don’t care about getting the best that they can get for themselves, and only want to vote sincerely to, in some way, maximize overall social benefit, and would therefore rate sincerely—and if they don’t object to the added difficulty of rating instead of ranking–then maybe a point-system like Score would be best, for that hypothetical, futuristic, utopian society.

Then, Score would be a good possibility. Collect the voters’ ratings of the alternatives, sum each alternative’s ratings, and elect the alternative with the highest sum.

But a moral philosopher named Rawls suggested that maximizing the sum of happiness is less important than minimizing the greatest unhappiness. So, one would want to minimize the greatest dis-satisfaction with the outcome. Using Score balloting, instead of just summing the scores, choose the alternative whose lowest rating on any one ballot is higher than the other alternatives’ lowest ratings. Of course family and organizational choices are often informally, implicitly, made on that basis. That could be called a “Rawlsian count”.

Another possibility, for a “near-Rawlsian” point-count would be to ask voters to rate each alternative  either zero, or with a positive number, or with a negative number (say, from -100 to 100, for example). Then, apply some magnifying-function to the negative ratings, to increase their magnitude, to make them into larger negative numbers than the ones that were actually on the ballots. In that way, a dislike is counted more strongly than a like.

Most likely, for that purpose, one would use a function that curves downward more, as the magnified negative rating takes on more negative values. There are various possible functions that would do. I’ll just name a few:

1. Power function
2. Exponential function
3. Hyperbola

They’re listed in increasing-order of their achievable abruptness of the increase in the steepness of their down-curving, as we go to more negative input ratings. (Strictly-speaking some hyperbolae, such as the one that I suggest for this purpose, are power-functions too, but when I say “power function” here, I’m referring to the more typical, non-hyperbola, non-asymptotic, power-functions.

Majoritarians and Ideal Majoritarians to Come

For the purpose of this overall survey of voting-conditions and their method-recommendations, there’s no reason to add more detail to that. But I’ll say more about those near-Rawlsian magnification-functions in “Voting-Systems for Non-Majoritarian, Unselfish, Sincere-Rating Conditions”. “Voting-Systems for Non-Majoritarian, Unselfish, Sincere-Rating Conditions “will follow “Voting-Systems for Ideal Majoritarian Conditions”, which will soon follow this article.