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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