[EM] Poll/Approval Strategies and Lotteries

[Forest Simmons]

Here's an idea that might be practical in some small group situation, and 
might be modified and adapted to more general use:

In its easiest to understand form it requires two passes (i.e. two trips 
to the polls).

In the first trip the voters simply vote for one candidate, presumably 
their favorite.

This first pass serves as a kind of binding poll with teeth in it; if the 
voters don't vote honestly it could bite back.

Accordingly, the results of the first pass are published before the second 
pass.

The threat is that the winner will be chosen by random ballot from the 
ballots of the first pass if in the second pass this lottery option turns 
out to be the Condorcet Winner.

The ballots for the second pass are approval style ballots, since they are 
sufficient for determining whether or not one fixed option is the 
Condorcet Winner.  You are asked to indicate which candidates that you 
prefer over that option, in this case the lottery option.

This gives a definite meaning to the phrase "approve all candidates that 
you would rather have than the election itself."

If no candidate gets more than fifty percent approval, then the lottery 
option is preferred by majorities over each of the other candidates, i.e. 
the lottery is the CW, which means that the actual winning candidate is 
determined by drawing a ballot at random from the first pass ballots.

If more than one candidate gets more than fifty percent approval, then the 
one with the most approval wins.


[end of description of basic method]


You can imagine several variations.  If Cardinal Ratings style ballots are 
used, then there is no need to go to the polls twice:

The first pass results are inferred from the ballots and tabulated.  The 
resulting lottery is used to calculate "above mean expectation approval 
cutoffs" on each of the ballots, so that the approval scores of the second 
pass can be inferred.

If ordinal ranking style ballots are used, then instead of "above mean 
expectation" we use "above weighted median" to calculate the cutoff as in 
Chris Benham's Weighted Median Approval.  In other words, this method is 
just WMA with a twist; if no candidate gets sufficient approval, then the 
result is decided by random ballot.

Of course, this method is subject to iteration.  If there are several 
candidates with more than fifty percent approval, then calculate a second 
lottery based on ballot preferences among these winners of the first 
approval contest, and then determine the above weighted median (or mean) 
approval scores based on this lottery (on the full ballots; remember 
"runoff without elimination").

If there are several candidates with more than fifty percent approval 
based on this new approval cutoff, then take the one with greatest 
approval, else use the second lottery to pick the winner.

Another variation is to infer a more sophisticated lottery from the 
cardinal or ordinal ballots as the initial lottery.  Random Ballot Smith 
might be an improvement over plain random ballot, for example. Jobst and I 
are working night and day without sleep to find better possibilities.

Another idea is (once you have a lottery) to include it as one of the 
candidates, and then use Condorcet methods to see if it ends up in the 
Smith set, etc.

I'm sure that you can see many different directions to go with these 
ideas.

Have Fun!

Forest