[Election-Methods] Improved Approval Runoff

[Chris Benham]

Diego Renato wrote:

> All one-round voting systems that allows ballot truncation are 
> vulnerable to bullet voting, resulting the same results of plurality 
> voting. For instance, suppose that some voter has A as his/her first 
> preference. S/he can vote like this:
>
> Approval: A: approved; B: rejected; C: rejected; D: rejected ...
> Range (0 - 100 scale): A: 100; B: 0; C: 0; D: 0 ...
> Preferential (IRV, Condorcet, etc): A>B=C=D=...


A voter never gets a better result for hirself in IRV by bullet voting, 
because lower rankings do nothing until the voter's higher-ranked 
candidates have been eliminated.
IRV meets "Later-no-Harm".

Also as has been pointed out, in all the methods you mention it only 
takes a small proportion of voters to max. score or rank more than one 
candidate to give a different
result from plurality voting. I regard Approval as vastly vastly better 
than Plurality (FPP) even if in practice nearly all voters bullet vote 
and the result is always the same
as if they all had.

> Additionally, there are several instances which only binary input 
> voting systems are reasonable. Complex systems are hard to adopt in 
> low-educated underdeveloped countries.

Yes, interesting problem.

> This system, called Improved Approval Runoff (IAR), has the goal to 
> resist bullet voting through simple ballots.
>
> Description:
>
> 1) On the first round, the voter can vote for as many or as few 
> candidates as desired.
> 2) If some candidate has more than 50% of approvals, the most approved 
> is elected.
> 3) If not, that candidate runs a second round against other candidate 
> - the most approved after a new count which the votes for the first 
> one are reweighted to 1/2.
> 4) The winner is the candidate who receives a majority of votes on the 
> second round.
>
> On computer simulations, the top-two approval runoff method selected 
> more times the Condorcet winner than any Condorcet method. I think 
> that IAR is slightly fairer than top-two approval runoff under real 
> voters.
>
> Any comments?


I think this is not bad for a simple method and a big improvement on 
"top-two approval runoff", which I long ago rejected as a strategy farce.

Parties with a chance of winning a normal approval election will run 
pairs of clones and ask their supporters to approve both of them.  Normal
plurality top-2 runoff is more vulnerable than IRV to the Pushover 
strategy, but approval top-2 runoff is much much more vulnerable again.
Voters who are confidant that their favourite or one of their favourites 
(with their approval) can qualify will have incentive to also approve 
all the
candidates they are sure that their favourite/s can beat in the runoff.  
If  a faction succeeds with this strategy then the final round will be 
between
their favourite and a  candidate with much less sincere support.  If  
more than one faction attempts it then it is just possible that both 
qualifiers will
be "turkeys" with very little sincere support.

> *push-over*
> The strategy of ranking a weak alternative higher than one's preferred 
> alternative, which may be useful in a method that violates 
> monotonicity <#monotonicity>.
>


> 2) If some candidate has more than 50% of approvals, the most approved 
> is elected.

This is understandable, but if more than one candidate has more than 
50%  approval then I would still like to see a runoff.  Maybe I'd like to
see a runoff in some circumstances even when only one candidate has 50+% 
approval.  This special rule of yours creates extra Compromise incentive
and also means that the result can be changed by adding or removing 
ballots that ignore all the viable candidates (just by changing the 
absolute size of
the 50% threshold).

> 3) If not, that candidate runs a second round against other candidate 
> - the most approved after a new count which the votes for the first 
> one are reweighted to 1/2. 


This prevents the final from being between a pair of clones from the 
same party. It makes the Pushover strategy a bit less effective because 
voters
can't have their first-round votes count at full strength for both their 
sincere favourite and the turkey. How did you decide on the reweighting 
figure
of 1/2?  Why not  "reweight" those ballots that supported the first 
qualifier to zero?  That would mean that Pushover strategists would have 
to take
some extra risk by not approving their sincere favourite in the first 
round (as in normal plurality top-2 runoff).

Chris Benham








> All one-round voting systems that allows ballot truncation are 
> vulnerable to bullet voting, resulting the same results of plurality 
> voting. For instance, suppose that some voter has A as his/her first 
> preference. S/he can vote like this:
>
> Approval: A: approved; B: rejected; C: rejected; D: rejected ...
> Range (0 - 100 scale): A: 100; B: 0; C: 0; D: 0 ...
> Preferential (IRV, Condorcet, etc): A>B=C=D=...
>
> Additionally, there are several instances which only binary input 
> voting systems are reasonable. Complex systems are hard to adopt in 
> low-educated underdeveloped countries.
>
> This system, called Improved Approval Runoff (IAR), has the goal to 
> resist bullet voting through simple ballots.
>
> Description:
>
> 1) On the first round, the voter can vote for as many or as few 
> candidates as desired.
> 2) If some candidate has more than 50% of approvals, the most approved 
> is elected.
> 3) If not, that candidate runs a second round against other candidate 
> - the most approved after a new count which the votes for the first 
> one are reweighted to 1/2.
> 4) The winner is the candidate who receives a majority of votes on the 
> second round.
>
> On computer simulations, the top-two approval runoff method selected 
> more times the Condorcet winner than any Condorcet method. I think 
> that IAR is slightly fairer than top-two approval runoff under real 
> voters.
>
> Any comments?
>  
> ________________________________
> Diego Santos
>
>------------------------------------------------------------------------
>
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>  
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