[Election-Methods] Improved Approval Runoff

[Abd ul-Rahman Lomax]

At 04:00 PM 8/15/2007, Diego Renato wrote:
>All one-round voting systems that allows ballot truncation are 
>vulnerable to bullet voting, resulting the same results of plurality voting.

"Vulnerable" implies that there is something wrong with this. It is 
not correct to claim that this gives "the same results" as plurality 
voting. That's only true if *all* voters bullet vote. And if that is 
what they want to do, who are we to say that they should not?

>  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=...

Yes. What's the problem? In a good method, if truncation results in 
no majority winner, that is, majority consent to the win is not 
apparent from the ballots, there should be a runoff.

>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.

I'm mystified as to why we should "resist" bullet-voting.


>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.

It seems with the reweighting that it is assumed that the voter only 
votes for two, otherwise why that particular reweighting?

I'm not sure I understand the "second round." The expression was a 
bit garbled, I suspect. I assume that the "second round" is not an 
actual runoff, but a recounting. As written, it would seem manifestly 
unfair to the first candidate, the plurality winner of the approval election.

There is no way to guarantee that a candidate gets "the majority of 
votes" except by redefining votes to mean something other than "the 
majority of voters approve this outcome of the election." (Top two 
runoff does it by a trick: the voters only have two choices, and any 
ballot which does not select one of them is discarded. This is 
actually a failure of democracy, election results, when possible, 
should always be ratified by a majority. That's what happens in small 
societies using full democratic process, this step is only skipped in 
large elections, supposedly for efficiency.

However, Asset Voting methods could make real runoffs and 
ratifications quite efficient.

>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.

Again, I don't think that's true. Approval is *not* guaranteed to 
pick the Condorcet winner, no matter how you slice it, and any 
Condorcet method, by definition, will. That is, a Condorcet method 
*always* finds the Condorcet winner if voters vote sincerely, and 
there are few reasons to treat the matter as if they will not.

however, the Condorcet winner is not necessarily the best winner; 
Approval may, indeed, select a better winner, as shown by social 
utility simulations. Approval begins the progression of Range 
methods, which match the very method of measuring what it means to 
have a good result. ("Condorcet Criterion" can be shown to manifestly 
make a poor choice under certain conditions, it really is not 
controversial. That is, a small society would *never* choose what the 
Condorcet Criterion would indicate should win, given sufficient 
knowledge, under certain conditions, basically those of a majority 
with a sufficiently weak preference and a minority with a 
sufficiently strong one. Who decides, properly, when such a condition 
should result in the violation fo the Majority Criterion?

The majority, but it is crucial that the decision be explicit.

What I have suggested is that Approval have a preference marker 
added. I called this A+; that is, Approval with a "Plus" indicator 
that shows preference. This marker could be used for more than one, 
but the general intention is that it would be used to show the 
Favorite. The ballot then indicates the set of approved candidates -- 
these are considered acceptable under the present conditions by the 
voter -- and the favorite -- or favorites -- as well.

However, initially the ballots are counted without regard to the Plus 
marker. It's an Approval election, initially. Now, with basic A+, 
that's it. The Plus marker is used for analysis of election results, 
allocation of campaign funding, and other informational purposes.

But having this preference information allows a new possibility, I 
called it A+/PW, for Approval Plus, Pairwise. If the ballots show 
that there is a *different* winner through pairwise analysis, using 
the Plus markers as well as the other Approval Votes, then there 
would be a runoff election between the Approval winner and the 
most-approved candidate who beats the Approval winner.

This version of Approval is Majority Criterion compliant, but through 
a trick: it's the majority in the runoff that counts. Nevertheless, 
this is far more democratic. It is much closer to an explicit 
ratification of the election.

I would also trigger a runoff if there were no candidate with 
majority Approval. If there was no candidate who beat the Approval 
winner pairwise, the runoff could be between the top two Approval candidates.

But Asset Voting is better.... And the Asset Ballot is extremely 
simple; it is a basic Approval ballot.