[EM] Advantages of the two-round system vs Schulze method and contingent voting

[Kristofer Munsterhjelm]

Peter Zbornik wrote:
> Hello,
> 
> an other question I wonder if you could help me with:
> For single winner elections we currently use the two round system, which 
> is equivalent to the Contingent vote providing that the voter does not 
> change preferences 
> see http://en.wikipedia.org/wiki/Two-round_system and http://en.wikipedia.org/wiki/Contingent_vote
> 
> <http://en.wikipedia.org/wiki/Contingent_vote>According to the table on:
> http://en.wikipedia.org/wiki/Schulze_method#Comparison_with_other_preferential_single-winner_election_methods,
> Contingent voting 
> <http://en.wikipedia.org/wiki/Sri_Lankan_contingent_vote> has no 
> advantage over Schulze method (apart from being a few dimensions simpler 
> in terms of vote count and understandability for the common person).
> Two-round voting (although widely used) is not listed in the table.
> 
> The questions are: 
> 1) Does the two-round system satisfy any criteria, which Schulze method 
> fails, apart from complexity and understandability and the option to 
> change preferences between election rounds?

If voters vote exactly the same way in both rounds, and there are three 
candidates, the two-round method is equal to IRV. In this case, it 
passes LNHarm while Condorcet does not.

If the voters don't, then it makes no sense to apply criteria to the 
two-round system as a whole. If you did, you could make the two-round 
system fail Majority unless it had a rule stating that there would be no 
second round in case of a majority preference. Just have a majority vote 
for A, the minority for B, then in the second round, have everybody vote 
for B.

> 2) What criteria does the two-round system satisfy that the Contingent 
> vote does not satisfy and vice versa?

See above. One can't apply criteria that applies to a single ballot set 
to a two-round method if the voters change their preferences between the 
rounds. If they don't, then the two-round method is simply the 
Contingent vote and so the compliances must be equal.