[EM] Range > Condorcet (No idea who started this argument, sorry; I am Gregory Nisbet)

[Kristofer Munsterhjelm]

Jobst Heitzig wrote:
> Dear Kristofer,
> 
> you wrote:
>> This is really a question of whether a candidate loved by 49% and 
>> considered kinda okay by 51% should win when compared to a candidate 
>> hated by the 49% and considered slightly better than the first by the 
>> 51%. A strict interpretation of the majority criterion says that the 
>> second candidate should win. The spirit of cardinal methods is that 
>> the first candidate should win, even though it's possible to make 
>> cardinal methods that pass strict Majority.
> 
> What does this "spirit" help when the result will still be the 2nd 
> instead of the 1st candidate, because the method is majoritarian despite 
> all cardinal flavour?
> 
> Again looking at my 55/45-example shows clearly that compromise 
> candidates are not helped by voters' ability to express cardinal 
> preferences but rather by methods which require also majority factions 
> to cooperate with minorities in their own best interest, as is the case 
> with D2MAC and FAWRB.
> 
> Would you bother to answer me on this?

Sorry about that. Because I've been away for some time, I've got a long 
backlog of posts, and I'm working my way through them.

Let's look at your example.

55: A 100 > C 80 > B 0
45: B 100 > C 80 > A 0

Range scores are 5500 for A, 4500 for B, and 8000 for C. So C wins. For 
Condorcet, A wins because he's the CW. So Condorcet is strictly 
majoritarian here, while Range is not.

You may say that, okay, the A voters will know this and so strategize:

55: A 100 > C 1 > B 0
45: B 100 > C 80 > A 0

In which case A wins. This, I think, is what Greg means when he says 
that a majority can "exercise its power" if it knows that it is, indeed, 
a majority.

As far as I understand, the methods you refer to aim to make this sort 
of strategy counterproductive.

Because Range isn't majoritarian by default, it doesn't elect A in your 
honest-voters scenario. I would say that from this, it's less 
majoritarian, because majorities don't always know that they are 
majorities. However, it's still more majoritarian than your random 
methods, because in the case that the majority does coordinate, it can 
push through its wishes.

To answer your question: the spirit helps because majorities are not 
always of one block, or the same. You have shown that it's possible to 
be less majoritarian than Range, though.