[EM] rating style ballots versus ranking style ballots for obtaining ordinal information

[Simmons, Forest]

I wrote ...

Ratings are a convenient way of providing for equal rankings and keeping the
ballots from becoming too unwieldy when there are large numbers of
candidates, as in a big election without primaries.

Mike replied:

But how is ratings more convenient than rankings? As long as the voters
understand that they can give the same rank number to as many as they want
to, and that rank numbers needn't be consecutive?

I reply:
 
Yes, as long as the rank numbers don't have to be consecutive.   In that case ratings and rankings are equally easy to construct since either can be directly inferred from the other.  If N is the maximum used rank, then the rating of a candidate is N minus the ranking of the candidate, and the ranking of the candidate is N minus the rating of the candidate, as long as the ratings allow sufficiently many slots.
 
The main reason to limit the number of slots is to keep the ballot from becoming too unwieldy.
 
Ranked ballot proposals will have to limit the number of allowed ranks for the same reason.
 
Since the two methods are equivalent (given the freedom of skipping ranks) why not go for the more intuitive rating approach, where low numbers correspond to low rates, or the familiar letter grading (with +/- allowed)? 
 
Other than that, another (more interesting) reason to limit the number of slots further (to three) is to mitigate the clone dependence problem of MDD methods:  when a clone cycle is forced to share three slots with the other candidates, a true clone cycle will be crowed into occupying two slots per ballot.  In that case, not all members of the cycle can be majority defeated by another member of that cycle.
 
Forest
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