Election Methods Draft Report

[Lowell Bruce Anderson]

Steve:

I think you made wise decisions concerning what to include in (and what to 
leave out of) the election-methods-list report.  Congratulations.

For whatever they're worth, I have a few minor suggestions.

First, in the general discussion of Pairwise Methods, I think that you 
should explicitly define and briefly discuss "pairwise ties."

Second, in the discussion of Smith, you should add the word "non-empty" to 
change:  "(To be more precise, the "best" group is the smallest group which 
can be found such that..." into:  "(To be more precise, the "best" group is 
the smallest non-empty group which can be found such that...".

Third, you should change:  "...the winner is the candidate..." to:  "...the 
winner(s) is/are the candidate(s)...", and change "elects the candidate 
whose largest pairing-loss is..." to:  "selects the candidate(s) whose 
largest pairing-loss is...", and so on, everywhere that a tie is possible.  
I agree that such ties will be rare in large public elections.  However, I 
think that the use of "good" single-winner voting methods is quite important 
in many different voting situations, not just in large public elections.  
For example, many votes are taken in governmental and quasi-governmental 
voting situations by:  legislatures, councils, committees, subcommittees, 
boards, panels, commissions, juries, delegations, etc.  Many of these 
"smaller" voting situations could easily result in ties.  Though perhaps not 
as important, similar comments can be made about votes taken in private 
voting situations.  Moreover, in some private voting situations, the entire 
electorate could be relatively small, which, of course, increases the 
likelihood of ties.  Finally, I think that people will generally want to 
examine small examples and run small test cases before they adopt a new 
voting method for large public elections.  Again, ties may be likely.  Note 
that by "ties" here I do NOT just mean cases in which exactly 1/N of the 
voters rank each of N candidates as being their unique ith choice for all i 
from i=1 to i=N, and N > 1.  I also mean, for example, cases in which 
Smith//Condorcet would result in a tie, but Smith//Condorcet//Plurality 
would not, and cases in which
Smith//Condorcet//Plurality would result in a tie, but 
Smith//Condorcet//Plurality-ext would not.

Finally, I think that names like Condorcet are in the public domain, and so 
it's quite reasonable for you to define "Condorcet's method" one way and for 
Hugh or me to define it slightly differently (e.g., differently only when 
ties or truncations occur on voter's ballots), just as long as we always 
clearly state the definitions we are using.  However, I think that when 
someone makes up a name that is clearly "brand new" in voting parlance, then 
others ought to either ignore that name or to use it has its originator 
defined it.  In particular, I made up the name "Regular Champion," and I 
defined it to be:  [Copeland]//[Plurality-ext]//Random, not 
Copeland//Plurality.  If you want, you can ignore Regular Champion, and 
(say) discuss Copeland-Plurality instead.  Alternatively, if you want, you 
could declare that every voting method you discuss is to automatically be 
read as ending in "//Random", in which case you could say that Regular 
Champion is [Copeland]//[Plurality-ext].  But Regular Champion is not 
Copeland//Plurality.  My objection here is purely definitional, it does not 
affect the recommendations.

Bruce