[Election-Methods] Voter strategic opportunity (/regret) simulations (was: Re: Corrected "strategy in Condorcet" section)

[Juho]

I reply to an old mail since I now checked my archives to see what my  
old simulator (that I mentioned) did and what kind of results it  
gave. I'll list the numeric results here, but please note that this  
was a rather quick coding exercise and the results have not been  
double checked. Don't assume the numbers to be correct until they are  
confirmed by someone. Maybe some of you will do something similar and  
confirm or challenge the numbers.

The simulation set-up was as follows.
- I wanted to see how often some voters / voter groups will benefit  
of strategic voting
- I divided the voters into n groups of similar size
- In each group all the voter opinions were similar
- Each group acted as one strategic unit in the sense that the  
simulation checked if this group could change the end result by  
voting strategically
- All different strategies were covered, which means that all  
alternative possible ways to vote were checked
- Voter group opinions were generated so that each candidate first  
got a random utility value, and then the ballot was generated using  
this information as a basis
- (The size of the group is not defined (could be one or whatever  
number))
- The utility values were taken from a given limited range of utility  
values
- Probability of ties depended on the used range of utility values  
(small number of alternatives => more ties in opinions)
- Two voter strategic opportunity values could be measured: (or  
"regret" values if we think the voters are strategic by nature :-))
1) Probability of one of the groups being able to improve the results  
by voting strategically
2) Probability of any of the groups being able to improve the results  
by voting strategically
- Note that due to the random votes the elections are very close and  
therefore startegic opportunities are more common than in real life  
where candidates and votes typically have clearer trends (instead of  
being purely random)
- Counter strategies, simultaneous strategies by more than one group,  
exact number of strategic voters required, probability of success of  
the strategy, etc. etc. were not analysed

Here is one set of results for you.
- Range of utilities = 100
- Number of candidates = 3
- Number of groups = 11 (odd number gives less ties and strategies  
therefore work better)
- Number of simulated elections = 5000
- Results are listed below as "result 1)" / "result 2)"
- Plurality 8.2% / 42.4%
- IRV 3.1% / 13.2% (in IRV all tied at bottom candidates were dropped  
at one time)
- Condorcet Minmax(margins) 5.4% / 21.2% (Condorcet strategic  
alternative votes had no ties (also other methods may have similar  
limitations))
- Condorcet Minmax(winning votes) 5.4% / 21.9%
- Range (2 values) 21.5% / 59.6%
- Range (3 values) 26.7% / 58.4%
- Range (10 values) 26.8% / 60.9%
- Range (100 values) 26.5% / 62.4%
- Normalised Range (2 values) 10.8% / 47.5% (=~Approval)
- Normalised Range (3 values) 12.1% / 43.2%
- Normalised Range (10 values) 9.1% / 35.7%
- Normalised Range (100 values) 8.4% / 34.1%



I did also some additional quick simulations to show some comparison  
points to the results above. Don't trust the results too much - 1000  
elections may not give quite stable results yet.

- 100 utility values, 3 candidates, 21 groups, 1000 elections
- Condorcet Minmax(margins) 4.9% / 20.6%
- Condorcet Minmax(winning votes) 5.0% / 21.2%

- 100 utility values, 3 candidates, 3 groups, 1000 elections
- Condorcet Minmax(margins) 5.6% / 13.3%
- Condorcet Minmax(winning votes) 5.6% / 13.3%

- 10 utility values, 3 candidates, 11 groups, 1000 elections
- Condorcet Minmax(margins) 3.8% / 19.0%
- Condorcet Minmax(winning votes) 5.1% / 26.4%

- 100 utility values, 3 candidates, 5 groups, 1000 elections
- Condorcet Minmax(margins) 6.9% / 20.9%
- Condorcet Minmax(winning votes) 7.1% / 20.9%

- 100 utility values, 5 candidates, 11 groups, 1000 elections
- Condorcet Minmax(margins) 13.5% / 47.3%
- Condorcet Minmax(winning votes) 15.0% / 49.9%


- There may have been some more limitations/simplifications than the  
ones that I remembered and listed above
- Please ask if I missed some essential parameters that are needed to  
define the simulation set-up

Juho


On Jul 27, 2007, at 11:51 , Kevin Venzke wrote:

>>>> 2) There are as well cases where winning votes are more  
>>>> vulnerable to
>>>> strategies than margins. So the question is not one-sided.
>>>
>>> However, it is pretty clear that margins has a worse FBC problem  
>>> than
>>> WV does. Simulations have shown this, but it can be argued
>>> logically as
>>> well.
>>
>> May be so. Is there some reason why FBC would be a key criterion in
>> this case? I made some time ago some simulations on margins and
>> winning votes on if some certain random voter group or any of the
>> voter groups could (from their point of view) improve the outcome of
>> the (sincere) election by voting strategically (in whatever way). The
>> simulation gave margins somewhat better results than to winning
>> votes. Maybe the results depend a bit on what one simulates.
>
> What kind of strategy did you implement? What did you consider a  
> "better"
> result?
>
> FBC etc. is important because if voters can't be confident that  
> they can
> safely vote sincerely, then the method is destroying information  
> before
> it collects it.




		
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