- Let me add my own definition of simplicity:

1) voters can easily understand how to use the ballots

2) voters, given internal preferences as to feelings toward each candidates,

can easily convert this information to the terms needed to fill out the

ballots.

3) Voters need no knowledge of anything other than the candidates themselves

to vote the most effectively. They should not need to understand the voting

method nor know anything about which candidates are most likely to win

4) There is no conflict of interest between expressing their internal

preferences, and voting in the most effective way toward the best results as

described by those preferences.

As to 3 and 4, these also make a big difference on the "consensus"

criterion. Its pretty hard to say that something reaches a consensus unless

you can predict how people (with given preferences) will vote, using any

mathematical model. Unfortunately, if you have a system where voters must

be well informed (about more than the candidates) to vote effectively, or

worse yet, where they may be conflicted between strategy and sincerity, all

predictions go out the window.

BTW, I believe approval fails 2 and 3 but passes 4, while everything but

approval and condorcet fail 2, 3 and 4. All of them can pass 1 with a good

ballot design.

On 12/11/05, rob brown <rob@...> wrote:

>

> Hi Carolyn

>

> I prefer Approval to Range on the simplicity factor, but not to Condorcet

> methods.

>

> At first you might think it Approval is simpler, and you are right that a

> typical 12 year old might have the easiest time with Approval compared to

> Condorcet.

>

> The problem is that by the time they reach 13 or 14, they start to see how

> complex it really is. "Like" vs."Dislike" sounds simple, but quickly

> becomes obvious that it is a relative term. Relative to the other

> candidates? Well, if you want to vote effectively, it's really "relative to

> who you think might win".

>

> Which means that to effectively fill out an Approval ballot, you must not

> only understand strategy, but have a good knowledge of who is likely to

> win.....in other words those who have the best knowledge of the polls will

> have a strong advantage.

>

> With Condorcet, on the other hand, it just asks you to rank them relative

> to each other, and knowledge of the polls or of strategy is not going to buy

> you anything (well, only in rare elections, and if you have incredibly

> accurate knowledge of the polls, and if you are really really smart, it is

> going to make a small difference to vote with anything other than utter

> sincerity).

>

> To vote effectively with Range, you need to know everything you need to

> know with Approval, plus have the additional knowlede that it is inadvisable

> to vote at anything but the extremes, i.e., you should treat it as

> Approval.

>

> -rob

>

> On 12/11/05, Carolyn <gusrabson@...> wrote:

> >

> > Of course if we are going to choose an electoral method we need to

> > have some criteria. We hope that we can find criteria that are

> > non-contradictory. Here are two criteria that I consider absolutely

> > necessary:

> >

> > 1. Simplicity. An average 12 year old child should be able to fill out

> > a ballot with no additional instruction.

> > 2. Consensus. Given two electoral methods the better one is the one

> > whose results are accepted by the most people.

> >

> > Now I have got to admit that I am an advocate of approval voting and

> > these criteria will favor approval voting. But I favor approval voting

> > because I accept these criteria rather than vice versa. My second

> > criterion does not consider the possibility that there can be degrees

> > of disapproval. I admit this � but I feel that in view of the sketchy

> > and distorted information available to the electorate any fine-tuning

> > of degrees of disapproval is spurious.

> >

> > Does anybody know which of Arrow's conditions Approval Voting fails to

> > satisfy? What about Range Voting?

>

>

[Non-text portions of this message have been removed] - At 10:19 PM 12/14/2005, warren_d_smith31 wrote:
>1. I do not understand Lomax's improved and different

Ah, this is irritating. I didn't say that "I will not discuss [the

>redefinition of "median". He says he will not discuss the

>case with median=max or min, but

>in fact that is exactly the case that matters the most

>and hence is the most essential to discuss.

extreme cases] as a refusal, but merely due to lack of time in the

writing of that post. I think I gave sufficient information that

Warren, certainly, or others, could apply the concept to the extreme cases.

>If Lomax has a new statistical quantity in mind which is

The two old favorites have their application. Yet the objection to

>better than both mean and median for our purposes,

>then by all means explain/define it simply &

>clearly and explain why it is better. I admit to a certain skepticism

>there really is something better than these two

>old favorites which has been floating

>arund unnoticed all this time, but could be.

Median analysis for Range voting is that Median doesn't work. It

doesn't work because of a certain limitation when fed discrete data.

It would work fine if the data were continuous, if, as in the real

world, somehow, voters expressed an exact number that was subject to

the chaotic influence of existence, so that no two numbers matched exactly.

Median is totally well defined, and very, very useful, in the

standard definition. It just needs a little extension to be useful in

the analysis of Range data where the granularity is finite and ties

can easily be produced.

>2. Lomax considers it "unlikely" that median and mean

Which is what I said. I don't expect distributions to be skewed in

>could differ significantly. In fact that is

>commonplace and occurs in "skewed" distributions,

the manner assumed by Warren. Yes, I could be wrong. It was just a comment.

>i.e. having a nonzero mean-centered third moment.

That has not been shown.

>Also, it occurs (massively) with approval-vote-style data,

>as we've just been discussing ad nauseum!

Now, as to the analysis of the extremes. Consider this a first

attempt. All that is necessary is that the data be spread. It could

actually be spread by a very small margin. What is important is that

it be spread so that every vote is a discrete and unique number. The

most obvious and simple way to do this is to spread it over the

half-interval evenly. However, unlike the other votes, this does

*not* produce the same mean and median for the data at that interval,

but I do think it behaves correctly. It rounds off correctly.

The only issue, really, is how it behaves in interaction with votes

for other candidates who are not rated by the same number of voters.

(and there is still the issue of what to do with blank votes.)

But I'd be happy to see that it behaves well if applied to matched

numbers of votes, i.e., no incomplete ballots.

My intuition is that the simple, even spread that I've suggested will

behave properly.

For one thing, it should produce the same results as Approval, if all

voters vote Approval style.

It is ironic that Mr. Brown seems to have missed that this is

precisely what he said he wanted: a system that takes Range data and

automatically casts votes to reflect that data. What this does is to

determine an optimal approval cutoff from the Range data, and then it

essentially uses that cutoff to convert the Range data into approval

data. Where the critical votes (at the median Range) are tied, it

spreads the data in such a way that the recalculated median generates

the same Approval votes as would exist if voters voted above and

below that median in Approval style.

I'm saying that it appears that this approach, as far as what is on

the wiki, has been completely overlooked. Rather, median was rejected

simply because of ties due to the integral nature of the data.

(By the way, using higher granularity range does not solve the

problem, because many voters will round off, or will vote approval

style, an extreme form of rounding off. Thus simple median ties would

remain quite common, as Warren noted.)

(I'm asking the resident math professor to approach this question

creatively, instead of dismissively. Is there a solution to the

problem? Have I suggested it or an approach to it? If not, *is there

another solution*?)