[EM] More uses for grade ballots

Forest Simmons fsimmons at pcc.edu
Mon Jan 28 14:26:45 PST 2002

Grade ballots allow each voter to grade each candidate on a scale of zero
to four using the standard grade designations F,D,C,B,& A, respectively.

Various ways of determining winners from voted grade ballots have been
suggested.  Here are two more:

(1) For each candidate two numbers are calculated; his/her grade point
average, and his/her minimum head-to-head score.

[Note well that these numbers are calculated before any candidate is

The winner is the candidate from among those with above average grade
point averages that has the highest minimum head-to-head score.

In other words, the grade point averages are added up and divided by the
number of candidates.  Any candidate whose grade point average is lower
than this average of averages is eliminated.  The other candidates are
compared on the basis of their minimum scores.

This is a kind of cross between CR and MinMax.  The two respective steps
are designed to find a candidate that has support that is both reasonably
high and reasonably wide. In particular, the second step discourages too
much inflation towards the extremes.

Note that the method satisfies the Pareto Criterion and the Reverse
Symmetry Criterion.

Now for the second method.

(2) Again two numbers are calculated for each candidate; his/her median
grade, and his/her lowest quartile grade.

As in method (1) the first number is used to make the first cut, and the
other number is used to pick the winner from among the survivors. 

As in method one, the second step ameliorates any incentive to inflate too
highly the grade of a compromise candidate.

If a "compromise" candidate cannot make the first cut without your A level
support, then that candidate isn't so hot after all. 

If the candidate makes the first cut, then your B level support will
probably be above the lower quartile level, and hence count as full
support in the second cut.

[If your B level support is above the lower quartile level, then that
candidate would, in all likelihood, win without any support at all from


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