[EM] Even more complex Sainte-Lague: strategy

[Kristofer Munsterhjelm]

So Lavabit decided to cut service instead of opening themselves to 
unspecified snooping. Thus I had to switch mail providers, and with lots 
of real world stuff going on too, I've been quite idle this month.

So let's fix that by showing what I've been thinking about regarding 
Condorcet-type Sainte-Lague methods. And since Jameson said that it's 
better to write multiple posts instead of one long post on many 
subjects, I'll split my long document into parts.

There's strategy, where I noticed strategy. Then there's a description 
of a quite complex Condorcet-SL hybrid that *almost* works (very close 
to generalizing correctly), and finally some examples of how that method 
mitigates the need for strategy in my example.

So, strategy:

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I have found out that voters may have reason to strategize in 
Sainte-Lague not only when there are few seats,  and not only when their 
honest first preference has no chance of getting a single seat, but also 
in other  situations. Consider the following example, where all 
candidates are parties:

549: pA
102: pM
349: pB
10: pM > pB > pA

If the last ten voters honestly vote for party M, then the outcome is 
that A gets six seats, M gets a single  seat, and B gets three. But if 
the last ten voters compromise for B, we get:

549: pA
102: pM
359: pB

and A gets five seats, M still gets the one, and B gets four. The last 
ten voters prefer this to the honest  outcome, so they have an incentive 
to compromise.

More generally, there's a compromising incentive in ordinary Sainte 
Lague, which shouldn't suprprise us since  it reduces to Plurality in 
the one-seat case. CPO-SL handles the most egregrious cases of these 
compromising  problems by reducing to Condorcet in the one-seat case and 
by also dealing in a Condorcet manner with parties that don't get a 
seat, but the problem still exists for parties that get slightly more 
than a seat.