[EM] Remember Toby

[fsimmons at pcc.edu]

There are only two single winner methods that are uniformly better than Plurality, i.e. that are better in 
some ways and worse in none.  These two methods make use of Plurality style ballots, and those voters 
who want to use Plurality strategy (marking only their preferred of the two frontrunners) can do so without 
incurring a worse result than they would get in a Plurality election.

The two methods are Approval and Asset.  My remarks in the first paragraph explain why neither of 
these methods is in any way worse than Plurality.  To see that they are in some cases better, consider 
the following points:

In the case of Approval, if many voter s also mark the candidates they prefer over their Plurality choice, 
the results will often be improved. 

In the Asset voting case, consider that when you trust your Favorite candidate’s ranking of the other 
candidates, you can mark you favorite and not worry about Plurality strategy.   It appears that between 
eighty and ninety percent of the voters would rather have their favorite do the ranking.  Where do we get 
that figure?  We get it from  Australia where the vast majority of voters just copy their candidate cards 
onto the ballot. 

In summary, we have shown that both of these methods are at least as simple and have at least as good 
results as Plurality by treating the ballots as Plurality ballots, and that obviously safe and beneficial 
departures from Plurality strategy yield significant improvements in both cases.  Therefore, these two 
methods are uniformly better than Plurality.

Although there are many other methods that are better than Plurality, there are no others that are 
uniformly better, i.e. no other method Pareto dominates Plurality.

When we propose a method to replace Plurality, if that method is worse than Plurality in any aspect at 
all, you can be sure that the opponents will focus on that aspect.

But who can rationally oppose a change to a method that is uniformly better than the status quo, except 
by proposing what they think is a better method?  But that supposed better method can be shot down if 
it is worse than Plurality in any aspect.  Take IRV, for example.  It has more complicated ballots than 
Plurality.  And unlike Plurality it fails monotonicity, just to mention two aspects.  No matter that its clone 
independence and later no harm features may completely compensate in the minds of some people; it is 
not uniformly better than Plurality.

Even DYN which is a hybrid that allows Asset voting at one extreme and Approval at the other is not 
uniformly better than Plurality, because the ballot is slightly more complicated.  In every other way it is 
better than Plurality, Asset voting, and Approval.   So far I have seen no method that is uniformly better 
than DYN, but the trouble is that DYN is not itself uniformly better than Plurality because it needs a two-
bits-per-candidate ballot instead of a one bit per candidate ballot.  Our voting public may not be ready for 
that much change in the ballot.  All of the other proposed methods except various three slot methods 
like MCA use more complicated ballots than DYN.

Is DYN too complicated?  If so, we are stuck with ordinary Approval or ordinary Asset Voting.  They are 
the only choices simpler than DYN that dominate Plurality.