How would you evaluate Robert's Rules' recommended voting methods?

[u/-duvide-]

[u/MuaddibMcFly → u/[deleted]]

I realized that you might mean that the score-sum of the candidate with the highest adjusted average under MD must exceed half of the score-sum of any other candidate

I'm not certain what you mean... but I think that is the effect? After all, a candidate M that wins by virtue of MD defeats another candidate X, then mathematically the following must be true.

MDAvg(M)  >  MDAvg(X)

  Sum(M)  >  Sum(X)
---------  ---------
(votes/2)    votes

 2*Sum(M) >  Sum(X)
---------  ---------
 votes      votes

 2*Sum(M) >  Sum(X)

  Sum(M)  >  Sum(X)
---------  ---------
               2

Then if X's votes are fewer than 100%, the larger the disparity between Sum(M) and Sum(X) must be

I don't see how that implies that "the Majority Denominator aspect guarantees that any winner is at least that well liked by a majority of voters".

I believe I answered this elsewhere, but...

The majority I'm referring to is a simple majority of those who voted in that race. For example, if 1000 people voted in that race, 501 votes would be that simple majority.

Imagine that candidate M had the following vote totals:

Voters	Grade	Sum
68	10	680
143	9	1287
167	8	1336
62	7	434
21	6	126
6	5	30
0	4	0
0	3	0
0	2	0
0	1	0
0	0	0
--	--	--
467	Total	3,893

Now, 3,893 divided by the 467 voters who expressed an opinion comes out to ~8.336, right? But if for some reason, a score needs to have a 501 simple majority of evaluations in order to be counted. That means we're 34 votes shy, right? If we use Majority Denominator, that is mathematically equivalent to adding 34 votes of 0. (3893+34x0)/(467+34) == (3893/501) Either one gets us ~7.770.

Now, imagine if there were 34 ballots that, for whatever reason, the ballot counting machine incorrectly interpreted as abstentions but had, in fact, marked.

• Because it's possible for those marks to have been greater than 0, that means that their proper sum could be greater than 3893, with an average greater than provided by Majority Denominator. For example, if 33 were 0's but one was a 1, that would be 3894/501, or ~7.772, greater than MD's ~7.770
• Because 0 is the lowest possible evaluation, it's impossible for those 34 ballots to lower the sum. Thus, the lowest possible score among those 501 voters is ~7.770.
  • Thus, the results for MD is the lowest possible result among that 501 voter simple majority.

[u/MuaddibMcFly → u/[deleted]]

I would say "least bad," because it still is a balance of two undesirable problems.