[EM] Student government - what voting system to recommend?

[Juho]

On Apr 24, 2007, at 6:48 , Abd ul-Rahman Lomax wrote:

> At 06:37 PM 4/23/2007, Juho wrote:
>> Another explanation to the emergence of Approval style strategic
>> voting is that an individual voter might learn that, in a case where
>> there are only two candidates that have chances of winning the
>> election, voting A=9, B=0 instead of A=5, B=4 makes his/her vote 9
>> times stronger.

> A voter "might learn this?" Why didn't the voter know this from the  
> start. *Of course* voting the extremes is a strong vote. The  
> question is why you'd cast a strong vote if your preferences are  
> weak. Why? Because you want to "win"?

Many voters want that.

The reason why I talked about learning is that Range is often  
described so that the first impression voters will get is that they  
"should" put their sincere ratings on the ballot (and they would not  
be aware of how to vote with full strength).

> First of all, we think that it will be common knowledge that if you  
> don't vote the extremes for at least one candidate on either side,  
> you are casting a weak vote.

In most cases any use of intermediate values makes the vote weaker  
than it could be.

> Nobody is recommending that truly weak votes be cast. (But some  
> people may want to cast them anyway, and they should be able to.  
> Consider it a partial abstention, and many people abstain from this  
> or that race now.)

That's ok. Weak votes and abstention can be options for the voters.

> If A was the favorite, why in the world would the voter vote A=5 in  
> the first place?

The voter didn't find him/her "excellent" but just "reasonably good".  
With fully sincere (utility based) ratings maybe no candidate gets  
the max or min score.

> What is continually asserted here is that voters with weak  
> preferences will somehow decide to vote strategically.

I assumed that voters with strong wish to win, or those that  
(strongly) want to counter the ones that vote with full power, would  
vote with full power ("strategically"). This behaviour may make also  
the originally "weak preference" more radical. Voters that  
intentionally want to cast a weak vote (and that are ok with others  
using strong votes) would not be affected.

> Look, if there is an election, and I sincerely rank A as 9 and B as  
> 8 (and other candidates lower than that, let's say zero) and B  
> wins, I'm happy! That's an excellent outcome! The danger comes in  
> quite the opposite direction from what Juho proposes. Suppose I  
> rate B as 8 and C wins, with B being the runner-up. Close runner- 
> up. I might regret rating B at 8.

I believe this voting pattern os in line with the Approval style  
strategic voting that I discussed.

> If you vote Approval style, you fail to express your true  
> appreciation of the candidates, and this can backfire.

Yes, but typically/statistically Approval strategy improves the outcome.

> It is just as reasonable to consider that Range elections will move  
> *away* from Approval-style as that they will move toward it.

A simple example of this would be nice.

> I expect that they will start out, actually, as close to Approval  
> for many voters. Smith thinks differently, and I really don't know  
> which of us is right. He's got reasons to think his way. We might  
> both be right. I.e., many voters, maybe most, will vote Approval  
> style, and it will be bullet voting. But there will be quite a few,  
> from the start, who do something different.

I think much depends on the media and other discussions before the  
elections.

> I say that we are not going to really know until we see real  
> elections using Range. The alleged devolution to Approval is not a  
> serious harm. It would only mean that some ballot space and a  
> counting effort had been wasted.

Yes, Range could be roughly as good as Approval (with some wasted  
effort, and ability to cast weak votes). The biggest hiccups might  
come in the form of people realizing that their vote was weak  
although they didn't understand that when they voted, or if some  
candidate won as a result of efficient use of strategic voting.

>> Rating the least preferred candidate at 0 reduces the probability of
>> that candidate getting elected (and doesn't carry any risks with it).
>
> But from the conditions of the problem, there was no risk of that.  
> No, I don't buy it. (By the way, none of us involved with Range  
> would recommend giving the "least preferred candidate" any other  
> vote than the minimum. I assumed that PW was being given a 1  
> because voters somewhat liked him, there were *worse* candidates  
> involved.

There were no worse candidates involved. The voter liked PW somewhat.  
But since PW was the least liked candidate and the voter wanted to  
avoid electing him, giving him 0 was a perfect solution. (I thus used  
sincere utility based ratings instead of normalized ones.)

(If the probability of PW getting elected is strictly 0%, then any  
rating would be equally good.)

> In the two-party environment, Range strategy, like Approval, is  
> pretty simple. It's the three-way race which is trickier.

Pure Approval strategy may not be the best in Range always. If three  
leading candidates all get 33% support in an opinion poll and my  
sincere ratings for them are 8, 7 and 6, I might vote (strategically)  
max, half and min. But in general Approval strategy is close to  
optimal (strong vote) strategy and sincere ratings (sincere utility  
based or normalized) are not.

>> > If you are going to propose that Range will *reduce* to Approval,
>> > you will have to use reasonably likely scenarios.
>>
>> I think the vote strength argument that I presented above is quite
>> generic and applies in all typical elections - assuming that we talk
>> about competitive elections where the voter wants to do his/her best
>> to make his/her favourite alternative win.
>
> But this contradicts the assumed initial sincere vote! If you want  
> this, why would you vote A=9, B=8 in the first place? By voting  
> this way, you are saying that B winning is almost as satisfactory  
> to you as A winning!

The voter voted originally sincerely since voters were given the  
impression that they should write one's sincere preferences on the  
ballot. Candidate B winning would be quite satisfactory to this  
voter. The voter however wants to make A the winner if he can choose  
between A and B. If A and B were the only candidates, voting A=max,  
B=min would be also risk free.

> I think that people can and will understand that democracy is often  
> about making compromises. It is *not* about crushing the opposition!

I agree, but competitiveness exists despite of this, and that may  
lead to voting with maximum power etc.

> "Vote -1 to vote against a candidate, vote +1 to vote for the  
> candidate, and vote zero or leave a candidate unrated to have an  
> intermediate effect. The candidate with the greatest sum of votes  
> will win."

Note that negative votes carry some risks. Let's say there are three  
major parties with one candidate each, and many totally unknown  
candidates. All major parties are afraid of each others and will give  
lots of negative votes to both competing party candidates. The sum of  
all major party candidates may go below 0. Some unknown candidate is  
mentioned only in very few ballots (let's say his/her family members  
supporting and one neighbour opposing). His score will however be  
positive and he will be elected, not the well known candidates whose  
score was negative.

> [I suggested that there be a runoff between the Range winner and a  
> Condorcet winner, if they differ]
>> Let's assume that a Condorcet winner exists. In this case this method
>> could be said to be a method where the voters are given a second
>> chance to think again if the Range winner could be seen as a "good
>> compromise" even though the majority could easily vote as in the
>> first round and elect the Condorcet winner.
>
> Yes. That is, the original ballot analysis showed that this C.  
> winner was rated higher than the Range winner on a majority of  
> ballots.
>
>>  I'm not sure this method
>> would be a very practical method in real life large elections but in
>> principle the idea of "recommending" the Range winner to the voters
>> is a positive idea. Some strategies where people would try to
>> influence who the Range winner will be could take place (i.e. the
>> Range winner of the second round would not be the sincere range  
>> winner).
>
> I think Juho means that the Range winner of the *first* round would  
> not be the sincere Range winner. If there is a second round, it is  
> not held as a Range election. It is a straight which-of-these-two- 
> shall-be-elected vote. Voters will know, this time, if the first  
> election was sincere, which candidate will be most broadly  
> acceptable. Which is more important to them, for their preference  
> to win or for the most broadly acceptable candidate to win?  
> Majority rule.
>
> I'd suggest that if their preference was weak, the majority might  
> prefer the Range winner, on reflection. But if their preference was  
> strong, they might insist upon it.

If the first round votes were sincere the Condorcet winner will be  
preferred over the Range winner by majority (since the definition of  
Condorcet winner says so). The Range winner would however be better  
if measured as sum of satisfaction of the voters (if that is what the  
voters marked in the ballots). The opinions could however change  
before the second round as a result of publishing the fact that there  
was a Range winner that was different from the Condorcet winner, and  
the range winner could be supported by a majority at the second round  
(depends on the level of competitiveness etc.).

Juho




		
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