[EM] Two round system (improved Approval version)

[Chris Benham]

Juho,
I see from the "Method support poll" that you are  "close to 
supporting"  a  "Two round system".

I  regard the  normal  version of this, where both rounds are by 
Plurality and the top two from the
first round run off in the second, as pretty awful. The only criterion 
compliance advantage it has
over FPP is  Condorcet Loser, and generally the only thing good about it 
is that its equivalent to
IRV when there are three (or fewer) candidates.

One attempted improvement I've seen suggested  is to use Approval in the 
first round, and then
have the two most approved candidates run off in the second. 
Unfortunately that would be a
strategy farce because rich parties with some hope of  coming first in 
the Approval round will have
an incentive to gain an unfair advantage by each running two candidates, 
plus many voters will have
incentive to engage in easy Pushover strategizing by approving both 
their sincere favourite/s and the candidate
that they think their favourite can most easily beat in the second 
round. With too much of that, it is possible
that both of the finalists will be "turkeys".

I've recently had an idea on how to fix this without, say, having votes 
cast in the first round also count in the
second.

"The first round uses approval ballots. If there is a second round, it 
is between two candidates.
The first candidate to qualify for the second round is the Approval 
winner (A)
Of  those candidates B whose approval scores would exceed A's if  
ballots that approve both or neither of
A and B were altered so that they only approve of B, select as the 
second qualifier the candidate that is most
approved on ballots that don't approve A.
If there are none such candidates B, then there is no second round and  
A is elected."

Of course it is possible to "automate" this into a single-round method 
that uses ranked ballots with an approval
cutoff, but that would fail the Plurality criterion, the Irrelevant 
Ballots criterion and probably some (maybe more
serious) others. (Here by "round" I mean trip to the polling stations, 
with the results of any previous "round" in the
same election known to the voters.)

49: A
24: B
27: CB  (C>B, both approved)

Here the two finalists are B and C.   In the single-round version, C 
would win, failing the Plurality criterion.

A simpler version which is more often decisive in the first round but 
has a greater later-harm problem would
only consider the candidate that is most approved on ballots that don't 
approve the approval winner
(i.e. has the greatest "approval opposition" to the approval winner) for 
the  position of second qualifier.

In the above example that would be A, who would be rejected and so B 
would be elected in the first round.
But then the C supporters could have got C into the second round (with 
A) by only approving C.

One possible problem with this idea of mine is that it may not be widely 
seen/understood as legitimate that there may
be a candidate or candidates that  don't make it into the second round 
but have a higher approval score than the
second qualifier. The only way around that is to relax the insistence 
that only two candidates go into the second
round, and say that all candidates with approval scores higher than the 
second qualifier's also qualify for the second
round.  (If there are more than two candidates in the second round, then 
if we want to keep it a binary-input system,
Approval should be used instead of FPP.)

In the above example that would presumably mean that again B would be 
elected in the first round, unless perhaps A
volunteers to drop out, because otherwise all three candidates qualify.

I  bring this up for jurisdictions which for some reason want to keep 
having two election rounds, each with the voters
giving simple binary inputs.  Do  you think the French will like it?


Chris  Benham