[EM] A General Outline-Summary of Strategy for Approval and Score
email9648742 at gmail.com
Fri Sep 28 13:48:25 PDT 2012
(copied, with permission, from Democracy Chronicles,
by Michael Ossipoff
September 24, 2012
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
Approval Voting Example
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:
1) Computation-intensive count, probably needing machine balloting and
computerized counting, with consequent count-fraud problem
2) 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.
Table of Contents:
1. Brief Definitions of Approval and Score
2. Score Count
3. Approval and Score Strategy
.....a) With No Chicken Dilemma
.....b) What It Takes to Have a Chicken Dilemma
.....c) Dealing with the Chicken Dilemma
..........1) Why It Isn’t a Great Problem
..........2) Strategic Fractional Ratings (SFR)
.....d) Only Two Reasons to Give Fractional Ratings
.....e) How to Give Fractional Rating in Approval or 0-10 Score
4. Score Advantages
5. Approval Advantages
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
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
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
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
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
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?
Bottom-line: Approval is the best, most advisable, and most feasible
voting system proposal for official public elections.
The first U.S. president took the oath of office of the President of
the United States, April 30, 1789. AIt's been a long time without deep
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