Voting Game

Some exploratory code for a final project for the AI master course "Computational Social Choice" at the University of Groningen. The code currently implements the amendment and successive procedures from Barberà and Salvador (2017).

Results

Quota sweeps

The results folder contains the results of some of the experiments we have done on the influence of quota values. The quota_sweeps folder contains the outcomes of several experiments in which we generated random profiles and analysed the influence on the quota value on their outcome. Files are named according to the rule q-<RULE>-<PROCEDURE>-<AGENDA_SIZE>.log. Furthermore, four .csv files are available containing all results for the configuration indicated in the file name.

Random profile analysis

The random_analysis folder contains the outcomes of analysing the same four configurations mentioned above. In this case, 50 random profiles were generated and analysed, meaning that the outcomes of min(n², 7!) agendas were calculated to figure out how often the outcome from the non-sequential rule (Borda/Plurality) was the same as the outcome of one of the sequential procedures (Successive/Amendment). These files have on their first line the average percentage, followed by the percentages of every individual run.

Usage

Creating voting profiles

You can supply a voting profile as a .csv, .txt or PrefLib .soc file. For the .csv, the program expects column headers indicating the voter ids. Columns indicate the linear order of preferences, e.g. the file

1, 2, 3
a, b, c
c, a, b
b, c, a

represents the profile

1 │ a c b
2 │ b a c
3 │ c b a

When using a .txt file, the expected format is the following:

1: a c b
2: b a c
3: c b a

This represents the same profile as the one in the CSV.

For .soc files, the expected format can be found here.

Running a voting game

To run a sequential voting game, first create a game:

game = Game( type = GameType.AMENDMENT
           , agenda = ['a', 'b', 'c'] 
           , quota = 1
           , profile = Profile.from_txt("profile.txt")
           )

Then, compute the outcome:

outcome = game.outcome()

Analysing a voting game

To analyse a voting game, create an Analysis object:

profile = Profile.from_soc("profile.soc")

# You can optionally supply an expected winner
expected_outcome = profile.winner(Rule.BORDA)

analysis = Analysis( type = GameType.AMENDMENT
                   , profile = profile
                   , quota = 2
                   , expected_outcome = expected_outcome
                   )

Then, find all possible outcomes:

outcomes = analysis.outcomes()

If an expected outcome was specified, this will also print how often that outcome occurred. This can be seen as an indication of the manipulability of a game type in some situations: if the expected winner is often different from the winner of the game, then the agenda has a large influence on the outcome. Similarly, if there are many different outcomes for some game, this also indicates the game type could be manipulable.

🚨 WARNING 🚨 When analysing profiles with many alternatives, the number of possible agendas grows really fast: The number of possible agendas, i.e. all permutations of the alternatives, is the factorial of the number of alternatives. This program uses some multiprocessing tricks to try to speed up the calculation¹, but running the analysis on more than ~10 alternatives (depending on your hardware) is not advised. On my pc, analysing a profile with 9 alternatives with the successive procedure takes around 3 minutes (before multiprocessing: 13 minutes). Note: This seems to run into deadlocks sometimes. If the code runs for longer than you expect (and you probably shouldn't expect anything over 10 minutes if you're using a ‘reasonable’ number of alternatives), just kill the program.

Running experiments

(Still need to write documentation for this. See main.py for some details)

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^{1Throwing the problem more processes is not an ideal solution, of course, and there are likely many more elegant solutions to improve performance.}