[EM] election-methods Digest, Vol 37, Issue 14

[Abd ul-Rahman Lomax]

At 01:30 PM 7/18/2007, ws at cs.brown.edu wrote:
>About DYN, Condorcet then range, and range then top-two runoff: I'm concerned
>about using a complicated method for three reasons.

First of all, Approval is an excellent method, and minimally 
complicated, it's actually a little less complex in some ways than 
Plurality! (That is, all one does is to count the votes, there is no 
need to make what can sometimes be difficult decisions about whether 
or not to count a ballot; in another way Approval is a little more 
complex, if you are doing hand counting by sorting ballots into 
piles. You have to sort multiple-vote ballots separately. Not 
difficult, to be sure, but slightly more complex. But much simpler 
than any other reformed method we know of.)

Range is also quite simple: just count the votes and add them up. The 
Center for Range Voting does add in a "quorum rule," which in my 
opinion is a refinement that might never actually improve anything, 
it just adds complexity. My own proposal is just add up the votes. 
Makes it slightly harder for a dark horse to win, but that isn't easy 
anyway, and it is, in my mind, controversial if a dark horse, i.e., 
one not rated by enough voters to win with using Average Range 
instead of Sum of Votes Range, should have any advantage at all, and 
Average Range clearly provides an advantage.

Now, as to Approval or Range with runoffs, the added complexity is 
one which is already broadly accepted. It's *normal* in many 
jurisdictions, if the ballots don't indicate a majority winner, to 
have a runoff between the top two. So this is, in some places, status 
quo. And it does not complicate the ballot or counting, with 
Approval. With Range+2, it also isn't more complicated, but if the 
runoff is routine, it adds expense and difficulty. That could be 
addressed by setting an Approval cutoff (say 50% rating) and only 
holding a runoff if more than one candidate gets above 50%.

>1) Complicated methods have a lot of design decisions. Voters will 
>be unhappy if
>their candidate lost, but would have won if a design decision were done
>differently.

While there *are* design decisions, remember the status quo is that a 
method which is *clearly* awful when majority failure takes place is 
continuing to be used. We already have top 2 runoff in many places, 
and frequently it chooses the wrong top 2 (as in France) thus, 
sometimes, ultimately choosing the wrong winner.

"Voters will be unhappy if their candidate lost." There are some 
assumptions here. First is that voters won't be unhappy if their 
candidate lost under Pluralith. Second is that voters have a 
candidate, "their candidate." You mean, I presume, their favorite. 
But if the preference strength is small, they won't be quite so 
unhappy at all, in fact they might be quite happy with the result. 
And those are the conditions where a runoff might take place, 
conditions where the majority has a smaller preference strength.

*No matter what system you have,* there will be voters who will be 
unhappy with the results, because a different system will produce a 
different result. Why not choose a method that minimizes voter 
unhappiness? Another name for that is Bayesian Regret, and Range is 
designed specifically, to minimize it. But because of strategic 
voting, Range can fail to actually minimize Regret, and runoffs can 
detect this.

Range with a runoff is certainly not more complicated than a series 
of Approval election!

>2) Voters need to understand the voting method. IRV, approval and range are
>simple enough. Pure Condorcet is marginal. Anything more complicated is too
>complicated IMHO.

Range +2 is just as easy to understand as plain old Range. Range with 
pairwise analysis is, indeed, more complicated, but it actually makes 
Range come more into line with traditional expectations about 
elections (such as the Majority Criterion).

I have left open the exact design, so far, of the conditions that 
trigger a runoff, and the exact nature of the runoff, because there 
are indeed complex considerations, possibly. But the final choice 
should certainly have as a characteristic, ease of understanding and 
simplicity.

For example, here is a criterion for a runoff:

The votes on the ballots are added up and the candidates with the 
highest vote total is the Range Winner. The ballots are then examined 
to find if there is a candidate who is rated higher than the Range 
winner on more ballots than rate the candidate equally with the Range 
winner or lower than the Range winner. If there is such a winner, a 
runoff is held between the Range winner and this preference winner. 
If there are two such preference winners, the one with the highest 
Range total is the one chosen for the runoff.

This is extremely simple to understand. It means that if you rate one 
candidate higher than another, you are voting for that candidate over 
the other. And counting this is also simple, because you do not need 
to create the whole Condorcet matrix, you only need to look at part 
of it. I won't describe the algorithm here.

>3) When a flaw is found in a design, there's a natural temptation to 
>add another
>feature to fix this flaw. If you aren't careful, you can end up with a design
>that's still flawed, but is so complicated that you can't tell what the flaws
>are. Remember the KISS principle in engineering: keep it simple stupid.

Sure. However, with Approval and Range, we are bucking the Majority 
Criterion, which is about as simple as you can get. Problem is, the 
MC is flawed, because it fails to consider preference strength. But 
we can do both, preserve the majority criterion and still allow 
better results to emerge.

You want KISS, stick with Plurality. Of course, you *could* allow 
overvotes, which is quite simple, and this is, in fact, our present 
tactical recommendation: implement Approval, now! Details can and 
will be added later, and going for Approval now does not preclude 
using a more sophisticated ranked method, such as IRV or better, 
later, it is really only a matter of adding ranks and a method for 
using them; alternatively, one can add rating levels to get Range. I 
think there will be pressure, once we have Approval, for more 
flexibility in expression, and for good use of the information gathered.

But I think we should be aware that a very simple procedure for 
setting up runoff conditions, quite analogous to existing practice, 
also brings Range (and Approval) into full compliance, no quibbles, 
with the Majority Criterion, because unexpressed preferences, those 
which could not be shown in the original Approval Votes, or which 
were suppressed for strategic reasons in the original Range Votes, 
can come out, if the voters stick to them, which they might not.

It's *obvious* to me that this is an improvement of the method, and 
simulations confirm that. Whether or not that makes it politically 
feasible is another story, but existing practice, which already 
tolerates the expense of a runoff in many places when there is 
majority failure, makes me think that it is.