Forest W Simmons fsimmons at pcc.edu
Sat Mar 10 10:54:53 PST 2007

Suppose that the alternatives are three restaurants for lunch, and the 
preferences of the two friends are:

1 Italian>Mexican>>Thai
1 Thai>Mexican>>Italian

[The second voter seems to prefer hotter spices.]

Under D2MAC they would always end up at a Mexican restaurant for lunch.

This is fine if the first voter is deathly allergic to Thai food and 
the second voter is deathly allergic to Italian food. But suppose there 
are no such allergies and that MacDonalds is a tacit fourth 
"irrelevant" option that is not even on the ballot:

1 Italian>Mexican>>Thai>>>McDonalds
1 Thai>Mexican>>Italian>>>McDonalds

Adding it to the ballot puts the other choices in perspective.

In this case, how should we distribute the winning probabilities?

This shows (among other things) that a Pareto Dominated, Condorcet 
Loser is not always absolutely irrelevant.

At the other extreme, suppose the election is presidential, and one 
voter bullets for write-in X, and no other voter even approves X, and 
that the first ballot drawn is the bullet for X.  Then under D2MAC 
candidate X wins.

Even though this is not likely, it is troubling in the context of a 
presidential election.

Is there a way to modify D2MAC to make it more acceptable in this 

How about adding the rule that if no candidate is approved on both 
ballots, and just one of them is a "bullet," then the favorite of the 
other wins.  If both are bullets (and different), then additional 
random ballots are drawn to decide between the two.

Something like that?


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