[EM] CR style ballots for Ranked Preferences

heitzig at math.uni-hannover.de heitzig at math.uni-hannover.de
Sun Sep 23 12:37:55 PDT 2001

I think what most people mean when saying that Condorcet methods are


(a bad name in my opinion since it contains no information about how 
it's defined but instead contains a verbal evaluation that should have 
no place in axiomatics :-) is the following:

|| It may happen that when the electorate is split in two arbitrary 
|| groups and in both groups there is the same Condorcet winner (that 
|| means, when only the voters in the group are considered), this
|| alternative might fail to be a Condorcet winner for the whole
|| group.

However, what I can't see is why this should be of any importance.
Instead, it just shows that in order to determine the winner, one 
cannot divide the electorate into groups but must consider all voters


Now as for the "trivial" and "important" preferences. This is nothing
innate to preference ballots. It will always occur that in an election
some people care more about what they vote and others less, so it will
always be the case that "trivial" votes "cancel out" the more 
"important" ones. I think this is just a property of democracy unless 
you want to weigh votes.

However, one might argue that in pluratlity elections those voters
whose preferences are not enough important (that is, those voters who 
do not care enough) will simply not cast a vote at all, while with 
preference ballots they have to rank all or none of the alternatives, 
even those they feel they don't know enough about to make a reasonable 
choice between them.

I consider this a very profound disadvantage of "classical" preference
ballots. There is however a *very simple* (at least theoretically) way 
to solve this problem:

|| just allow voters to express that they are "UNDECIDED" about
|| certain pairs of alternatives. In other words: do not assume that
|| individual preference relations are complete, but allow them to be
|| any quasi-order (that is, any reflexive and transitive relation).
|| One can even allow cycles in individual preferences!

(Beware: Undecidedness can *not* always be expressed by simply tying
alternatives: I can very well prefer A to B without knowing how to
value C at all. If I had to express this by tying C to either A or B I
would unwillingly express a preference for C over B or for A over C!)

There are enough rules that can handle such kinds of preferences. One
example that is I think a chimere between IRV and approval voting:

|| In the first round, each alternative gets a weight equal to the
|| number of voters that value it "optimal" (that is, that do not 
|| strictly prefer any other alternative over it). Drop the one with
|| the smallest weight and erase it from all the individual preference
|| relations. Iterate until stable.

My GrouCho preference aggregator ( http://welcome.to/groucho ) uses a
different method that is more like Tideman's and Schulze's rules (see 
the preprint on that website).


(If this message occurs twice then this is because I posted it a 
second time since it didn't seem to work the first time...)

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