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

[Juho]

On Apr 26, 2007, at 17:42 , Abd ul-Rahman Lomax wrote:

>> One more example on Range (that takes the ratings into account but  
>> is vulnerable to some strategies). The example is as above but the  
>> numbers are a bit different to make it clear who the "font  
>> runners" are.
>>
>> Sincere opinions:
>> 40% - 10 ER 8 C 0 EL
>> 40% - 10 EL 8 C 0 ER
>> 20% - 10 C 5 EL 0 ER
>>
>> Actual ballots when voters exaggerate their votes and apply  
>> Approval style strategy after observing that EL and ER are the  
>> "major candidates" / "front runners" (and after assuming that the  
>> final decision will be between these two):
>> 40% - 10 ER 0 C 0 EL
>> 40% - 10 EL 0 C 0 ER
>> 20% - 10 C 10 EL 0 ER
>>
>> Range picks EL as the winner. The sincere opinions would have  
>> given C the best score but strategies changed the situation.

> In order to move this to EL as the winner, somehow the electorate  
> must collectively decide to go for party affiliation rather than  
> sincere ratings. Range critics, quite simply, assume that this will  
> happen. Why isn't stated.

My story in this example was simply that voters see the results of an  
opinion poll that shows the (relatively) sincere votes as above. The  
voters and media note that EL and ER are the most probable winners.  
Then the voters, that already know that Approval strategy is the  
strongest one, use the Approval strategy to achieve the maximum  
voting power. They need to make the decision between the assumed  
front runners.

This example is not really good in explaining why societies that use  
Range voting originally would turn into thinking in Approval style.  
It is more an example of what might happen when people already know  
that also most other voters will use Approval strategy.

C is a strong candidate in this example, it seems even stronger than  
you said => average ratings EL - 5.0, E.R - 4.0, C  - 8.4. This makes  
C so strong that it could be seen as one of the front runners by many  
voters. If C was seen as a front runner by sufficient number of  
voters then he/she would win also when Approval strategy is commonly  
used.

> That the center voters would unanimously prefer the left candidate  
> to the right, quite simply, makes no sense.

Yes. I did that for simplicity. Also the other votes are too  
unanimous to be from real life (assuming that this is a relatively  
large election).

> However, if they rate ER higher, but still not as high as EL, EL  
> still wins. What really doesn't makes sense is that the EL/ER  
> voters unanimously decide to derate C. Given that they sincerely  
> rate C nearly as high as their faovrite, this strikes me as so  
> unlikely as to be worth calling "impossible" in a real election  
> with more than a few voters.

Yes. Further considerations and discussions might in this example  
change the first impression that EL and ER with their 40% first  
preference support are not necessarily the strongest candidates. This  
example is an extreme one in the sense that C is a truly popular  
candidate but Approval strategy might still work.

Maybe the key question is which candidates will be identified as  
front runners. Also some other comments of yours are related to  
clearly identifying who the front runners are.

> EL is the Condorcet winner in both cases!

C should be the strongest with Condorcet and sincere votes.


In order to clarify what kind of scenarios more characteristically  
_lead_the_society_ to Approval style voting I give another more  
typical example. Here C is considerably weaker (and opinions of C  
supporters are split).

40% - 10 A 5 B 0 C
40% - 10 B 5 A 0 C
12% - 10 C 5 A 0 B
08% - 10 C 5 B 0 A

- Average sincere opinions: A=6.6, B=6.4, C=2.0
- It is now easy to conclude that the chances of C to win the  
election are small => A and B are the front runners
- B voters and media note that B supporters would win if they ranked  
A slightly lower
- Next opinion poll indicates that some B supporters have lowered  
their A ratings and B would win
- Next opinion poll indicates that some A supporters have copied the  
strategy and now A would win again
- Next opinion poll indicates that most A and B supporters have  
learned the idea and plan to vote strategically
- Also C supporters learn that their votes are important and they  
should exaggerate their A vs. B preferences to pick the better one of  
the two front runners
- In this case the C supporters will probably decide between A and B

As a result the final ballots will be close to the ballots below.  
Some voters still vote sincerely, either because they do that in  
principle or because thy have not learned how to vote strategically.  
A has higher chances of winning. This is based on the assumption that  
the sincere voters (due to principles or not being aware of the  
strategies) are evenly spread. If sincere voters are not evenly  
spread, then the opinion segments that have more insincere voters  
have more voting power.

40% - 10 A 0 B 0 C
40% - 10 B 0 A 0 C
12% - 10 C 10 A 0 B
08% - 10 C 10 B 0 A

This is a very basic example on how the strategic voting style might  
emerge. Once it emerges (and people vote in Approval style by  
default), also the first example could quite easily lead to the  
described end result. Once Approval style voting becomes common it  
may be difficult to make the voters use again the full range of  
values (that are available in Range).

>> In summary, all methods have some problems. One needs to estimate  
>> which problems are lesser and which worse.
>
> Indeed. The example given shows, however, that Range -- at least in  
> this example -- reduces to Approval if all voters exaggerate their  
> ratings. Which is actually a decent outcome.

Approval is quite decent. Therefore also Range may be too. Some  
remaining prolems are that 1) use of strategy replaces the sincere  
voting style of (sincere) Range with more strategic voting style, 2)  
the voters need to guess who the front runners and to take risks, and  
that 3) not all voters will learn the strategies and therefore  
insincere/strategic voters will to some extent be rewarded. (These  
points should be taken into account also when comparing the  
performance of Range and Approval.)

(I note that it is up to the definition of the method which votes are  
considered "sincere" and which "insincere". Also strategic votes  
could be called "sincere". I hope you can read the description above  
in the correct spirit. Terms could be also different. If Range was  
explained in a close to Approval style, a larger percentage of voters  
would probably be able to apply the strategies in the most efficient  
way.)

> Again, I have certainly not proven this, but this is my impression  
> and intuition. While I suspect that scenarios can be manufactured  
> which would show strategic (in Range, this only means exaggerated)  
> voting as converting a Range win into a Condorcet loser win, I  
> doubt that these scenarios would be at all realistic, and thus  
> unlikely to show up in randomly-generated voting patterns where the  
> patterns are based on issue or approval space. (I.e., are  
> relatively realistic.)

Ok, the Condorcet compliance of Range is another case. My  
explanations didn't cover this yet (unless you take the original  
example as one where Condorcet winner is changed to someone else).  
This Condorccet compliance evaluation could maybe mean checking how  
use of Range changes the (quite well known) difference between  
Approval and Condorcet. (One interesting issue in all comparisons is  
to check if voters are able to state their sincere opinion or if they  
better vote some other (strategic) way.)

> The explanations of IRV that purport to make it seem batter than  
> Condorcet seem to me to be thoroughly specious, essentially  
> manufactured by people who have already decided to back IRV for  
> reasons other than the superiority of the method.

To me one possible explanation behind the strong support of IRV in  
U.S. is that is is a compromise that allows the support to minor  
candidates to be expressed but still keeps the probability of major  
candidates winning high.

> "Core support" is a totally bogus argument.

The best explanations I have found (again for U.S.) is that in the  
presidential elections the election is not only about one person but  
that person is expected to replace half of Washington with new  
people. In some sense bigger "core support" helps in this duty. But  
on the other hand surely also a competent independent candidate can  
collect a good set of people around him/her. Of course, if the rest  
of the system is two-party based (e.g. legislative body) then the  
president will not get much support on that side (no "core support"  
there???). These arguments are country and use case specific and do  
not say much about which methods are good in general or in all/ 
typical/most environments.

> Range *also* allows the majority to rule.

Ok, if the voters go use the Approval strategies.

Juho




		
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