by Michael Ossipoff
In previous articles published on Democracy Chronicles, I have discussed Approval strategy, Score strategy, the Chicken Dilemma, Strategic Fractional Ratings (for the Chicken Dilemma), considerations favoring some methods over the others, and more. In this article I will summarize those subjects, putting them together in a numbered and lettered outline form in order to provide more clarity. I think that with this numbered and lettered outline-format, this article will be much clearer.
Though I might briefly mention things that I’ve already discussed, I won’t repeat long explanations of those things but will, instead, refer readers to the previous articles in which I discussed those subjects. So, rather than writing in detail about strategy topics that I have already discussed, I will outline them in order to show the relationship between the different topics.
The main focus of this article will be on Approval and Score—the feasible proposals—clarifying their strategy and the choice between them. For official public elections, Approval is the feasible proposal or perhaps Approval and Score. In my first article here (“Some Problems with Plurality”), I explained that Approval is the natural, obvious, minimal, but powerful improvement on the “Plurality”, “Vote-For-1”, method that is currently in use. Rank methods bring two feasibility problems:
- Computation-intensive count, probably needing machine balloting and computerized counting, with consequent count-fraud problem
- The vast variety of ways of counting rank ballots, making it difficult or impossible for any particular rank-count to gain agreement, acceptance, and adoption.
Approval and Score are feasible because of their easier, more secure, count, and the obviousness that results from their simplicity.
1. Brief Definitions of Approval and Score
Approval and Score are point systems. Point systems are voting systems in which voters can give to any candidate however many points they want to. The candidate with the most points wins. Approval is the 0–1 point system. The voter can “approve” (give 1 point instead of 0 points) to as many candidates as he or she wants to.
Score consists of the point systems with more than two rating-levels such as 0–10 Score or 0–100 Score. For example, in 0–10. Score, you can give to any candidate, any rating from 0 points to 10 points. Score was called “Range” for quite a while. Score is the name most commonly used now, however “Range” will often be seen—mostly in older articles and postings. Score was also previously referred to as “Cardinal Ratings.”
2. Score Count
The obvious way to count Score, when processing each ballot would be to read that ballot’s rating of the ballot’s first candidate, and then to add that rating to that candidate’s running total. But count-labor equals count-fraud opportunity. Is there an easier way to do the big—hopefully open and public—hand-count for Score?
Well, suppose that the method is 0–10 Score. A better count method would be what could be called an “instance-tally”: For each candidate, keep tallies of the number of ballots giving 0 points, the number of ballots giving 1 point, the number of ballots giving 2 points, and so on. In other words, for each candidate, for each rating level available, keep tallies of the number of ballots giving him/her that rating. That means that, in 0–10 Score, you’re keeping 11 tallies for each candidate.
When processing each ballot, if it gives P points to candidate C, then increase C’s P-point tally. Then look at the ballot’s rating of the next candidate, and do the same. In that way, the counters aren’t adding the ratings to running totals. They’re just incrementing some tallies. If there are NC candidates, then, in 0–10 Score, there will be NC multiplied by eleven tallies. That’s a manageable number of tallies.
But Approval is much better in that regard, because there is only one tally for each candidate (no need tally the number who didn’t approve him—for that matter, Score could similarly get by with 10 tallies for each candidate, instead of 11). Of course Score 0–100 would require a lot more tallies. For that reason, 0–10 Score looks a lot more feasible than 0–100 Score. Anyway, after the public Score count, each candidate’s 10 or 11 tallies could easily be published and posted. Then, from those, anyone could determine the winner. Take a look at this example of Score Voting:
3. Approval and Score Strategy
a) With No Chicken Dilemma
This information can be found in the article entitled “Some Problems With Plurality”, toward the end, under the heading “Approval Strategy.” Basically, if you are certain that there are some candidates that you like, or trust, but not the rest, then approve them. If there are some candidates who are outright unacceptable, and they could win, then approval (only) all of the acceptable candidates.
If there aren’t unacceptable candidates who could win, and you want to vote strategically, approve the better-than-expectation candidates. For example, you could ask yourself, for each candidate, “Would I rather appoint him or her to office than hold the election?” If so, then approve him or her, because she’s better than what you expect from the election. But don’t be pessimistic about what you expect.
I claim that voting is a matter of optimism. First, your judgment about your expectation should be optimistic. Then you should approve only candidates who are better than what you expect from the election. Of course, by helping those better-than-expectation candidates, you’ll pull your statistical expectation upward. Better outcomes come with optimistic voting. The results will reflect your optimism.
If the election is by Score, then give maximum points to the candidates whom you’d approve if it were an Approval election; give minimum points to the others. Of course, in 0–10 Score, the minimum is 0, and the maximum is 10.
b) What It Takes to Make a Chicken Dilemma (I suggest four requirements for a Chicken Dilemma)
b1) The candidate in question should be someone who qualifies for approval by the considerations discussed above in a)
b2) His/her supporters like your candidate better than some candidate whom both factions like less than each other’s.
b3) But they’re likely to strategically 0-rate your candidate, taking advantage of your help for theirs.
b4) You care. (Maybe you just want to defeat Worst, by max-rating Compromise, even if his/her supporters defect. Or maybe it’s more important to show them that defection won’t work, to give Favorite a fair chance.
c) Dealing With the Chicken Dilemma
c1) Why it isn’t a great problem
There are a number of reasons why the Chicken Dilemma won’t really be a problem in Approval or Score: The other faction will know that your faction won’t help them next time if they defect. It’s difficult or impossible to keep defection secret, due to conversations, discussions, media discussion, etc. Parties or candidates can make non-defection promise agreements. Tit-For-Tat strategy is available (Over time, do as the other faction did last time—co-operate or defect, as they did).
c2) Strategic Fractional Ratings (SFR)
I’m speaking of a strategy for your whole faction, not just for one voter. If there is a Chicken Dilemma, regarding a certain candidate (“Compromise”), you can give to him/her some little “fraction-of-max” boost, enough to have a good chance of closing the gap between Compromise and Worst if Compromise is out-scoring Favorite‑—without being enough to be unduly help Compromise beat Favorite if Compromise would otherwise score lower than Favorite.
Obviously the above is a matter of pure guesswork—intuitive and subjective. The paragraph before this one tells the purpose of SFR. It doesn’t tell you how to judge the right fractional rating. That’s guesswork. But Compromise’s faction doesn’t have better information than you do. And so your guess carries some weight. The defection deterrence of SFR is genuine.
In an earlier article I discussed some types of faction-size assumptions and estimates that you could make, and suggested some formulas that you could use for SFR, based on those assumptions and estimates. However being based on estimates (guesses, really) that formula approach is really no more objective than the pure guesswork that I described in the paragraphs before this one. Use the formula approach only if you like it better. I prefer the direct pure guesswork approach described in previous paragraphs.
d) There Are Only Two Reasons to Give a Fractional Rating
d1) If there is a Chicken Dilemma
d2) If you don’t feel sure about whether a candidate is someone, whom you should approve, based on the considerations that I discussed under “If there isn’t a Chicken Dilemma”.
For instance, say it feels like a 50/50 (50% percent probability) chance that candidate X should be approved. Then give to him/her a fractional rating of 50 percent of max. And if it feels like a 75 percent chance that he or she should be approved, then give him/her .75 max as nearly as the Score version will allow. In 0–10 Score, you can give a candidate .5 maximum by giving him/her 5 points. You can give him/her .75 maximum by giving him/her 7 or 8 points (flip a coin). As for Approval, I get to that next:
e) How to Give a Fractional Rating in Approval or 0–10 Score:
Say the method is approval, and you want to give a candidate .7 maximum. Put 10 numbered pieces of paper in a bag, and randomly draw one out. If you’ve numbered the pieces of paper from 1 to 10, then approve the candidate if the number on the paper is not more than 7…that is, if the number is from 1 to 7.
If you’ve instead numbered the paper pieces from 0 to 9, then approve the candidate if the number you’ve drawn is less than 7. But suppose you wanted to give him/her .87 maximum? For this you want to number the pieces of paper from 0 to 9. Draw a number, and write it on a sheet of paper. Return the number to the bag. Shake the bag and draw again. Again, write the drawn number on the sheet of paper, directly to the right of the 1st number. If the number you’ve written is less than 87, then approve the candidate.
What if the method is 0–10 Score and you want to give a candidate .87 maximum? Do as I described when, in Approval, you wanted to approve a candidate with .7 probabilities. But here, you want to, with .7 probability, give the candidate 9 points instead of 8 points. So, (with the papers numbered from 1 to 10) if the number you draw is from 1 to 7, then you give the candidate 9 points instead of 8. Otherwise, you give the candidate only 8 points. Of course, if the papers are numbered from 0 to 9, then give him 9 points instead of 8 if the number drawn is less than 7.
4. Score Advantages:
Score’s more flexible ratings better allow the voter to do exactly as he or she feels. With the stark, all-or-nothing choice that Approval calls for, if the voter doesn’t make a good choice, then his/her choice might be really bad. But, in Score, the voter can give his/her best fractional estimate of what’s best and, not having to make the stark, all-or-nothing choice, a misjudgment won’t be as bad. I emphasize that the voter can give fractional rating in Approval too, probablistically, as described above, but fractional rating is easier in Score, built right into the balloting.
I used to criticize Score (and no doubt some still do), claiming that it encourages a voter to give fractional rating in a situation where his/her best strategy should (as described above) be an extreme rating, such as a 0 rating. I used to say that a more strategic voter could take advantage of him/her, by 0-rating his/her candidate. It now seems to me that that argument is fallacious: If the method were Approval, how do you know that that voter wouldn’t approve that candidate, giving him/her even more undue support? As I said above, the easy flexibility of Score would mitigate, soften, and minimize a voter’s misjudgments.
5. Approval Advantages:
First, as I said, in Approval you can give fractional rating, a fraction of max, probablistically, by drawing a number from a bag. How hard is that really? In a public election, with thousands or millions (or even hundreds) of voters, a probabilistic .7 rating, by a faction, is effectively the same thing as a .7 rating in Score.
And, as described above, under “Score Count”, Approval’s count is much easier and simpler than any Score count can be. Even the best and fanciest method (I consider Symmetrical ICT to be the best) won’t do you any good if the count is fraudulent. By that principle, Approval’s simpler, easier count is the all-important consideration.
If a voter wants to give fractional rating, it’s much better to give each such voter a little more to do than to give the counters more to do. That’s because one or more counters might abuse that greater opportunity for fraud. And what’s wrong with letting the fractional-rating voter have closer do-it-yourself involvement with that fractional rating that Score would have provided ready-made? Do we really need that ready-made luxury?
Approval and Score Election Bottom-line: Approval is the best, most advisable, and most feasible voting system proposal for official public elections.
Also see our entire section called Voting Methods Central.