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Mathematical Simulation Of Election In Democracy – India and USA


For long it has been said that democracy is when 51 idiots rule over 49 wise people. Let us see how true that statement is.

Game: 100 people vote for 2 candidates
Objective: Win votes more than the other candidate.

This statement assumes that in the system called democracy, the preferences are perfectly random and independent of each other. That is all 100 people vote purely from their own viewpoint where each voter votes for the person he/she really likes and nothing else affects their voting preference.

Now consider that 10 people out of these 100 started sticking together as a group and started always voting together. What happens is every candidate trying to win the game, has now different stakes in this group and the rest of the people.

Game theory states that provided the remaining 90 people vote randomly, every candidate will try to win the votes of these 10 people. Once votes of this group are won, the candidate has to work to get the remaining votes. The remaining votes are still random, assuming that the pursuit of the bunch of 10 votes has not affected either candidate’s chances of getting any of the remaining 90 votes. Indeed this assumption is true in most of the cases, since both candidates will be engaged in pursuit of these 10-vote-bunch, and both will be equally at advantage or disadvantage because of the pursuit.

So in this case, the 10 people actually end up ruling rest of the 90 people. The policies will be in favor of these 10 people, even if they are at conflict with the rest 90 people.

Conclusion: In democracy it is not the majority, but the group that provides the biggest shift from pure random outcome to pure determined outcome, is the group that wins. Under ideal conditions, this most effective group just happens to be the majority.

This is happening to a lot of extent in Indian democracy. The creating of one special interest group nearly breaks down the whole principle of democracy. The only antidote to this is creation of multiple special interest groups that are as random from each other as possible. One special interest group and remaining random group gives the candidates a simple strategy to “game” the system (or in better words, to win the election.) Creation of multiple special interest groups makes the “gaming” or “manipulation” of the system incredibly complex, thus forcing the candidates to rely on their agenda rather than following simple manipulation strategy.

This is how USA democracy system works. In USA democracy, each state gets some particular number of seats in senate. California has (I think) 51 seats. So if a candidate wins 26 seats in California, all 51 seats are awarded to the candidate, thus creating a special interest group. Thus even a smaller state means a bunch of senate seats, so cannot be ignored by a presidential candidate.

Perhaps this can be simulated mathematically as a game to figure out which system is better for India, two party system or multi party system.

If I have to simulate this as a game, this is how it would look like.

Things to evaluate:
How do the following factors affect the success or failure of election
1. Number of candidates (2 party or multi party system)
2. Number and sizes of special interest groups.

Entities:-
1. Voters – The voters will be represented by one big long array. Each voter has three attributes
a. Voter ID
b. Will vote- absent
c. if (will vote) then voted or not voted
d. special interest group id (random group, sp int gr 1, sp int gr 2, etc)
e. Like or dislike for each candidate – array of booleans

2. Candidates:-
attributes
a. Candidate ID
b. no. of votes won
c. array of special interest groups the candidates has secured.

3. Special interest groups-
attributes
a. Group ID
b. array of voters subscribing to that group.

Algorithm:

1. N no of Voters generated
2. M no of Candidates generated
3. L no of Special interest groups generated
4. Election begins
while (voted + absent != total voters)
{
for ( each of the candidates in the array)
{
candidate 1 randomly picks one voter
if the voter = absent candidates picks another voter till “will vote” voter is found
candidate sees if voter belongs to the special interest groups won by that candidate, if yes, candidate wins that voter, if no candidate loses that voter. If the voter does not belong to any special interest group, one random Boolean is generated to decide if the voter will vote for the candidate or not.
if the voter votes for the candidate, the candidate votes won += 1
}
}
5. Result declared- the candidate winning max votes wins.

So if the candidate that won is disliked by more people than liked, then the election process failed.

Will do this when I find some time. In the meantime if you read my post and if you try this simulation, let me know the results. When I was a student, I had a copy of Matlab software. I don’t have it now. I wanted to download open source alternatives like Scilab. No time to download and learn.

Recently president A P J Abdul Kalam stated that India should move to two party system. Running this simulation will provide a good idea about how effective will that be.

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6 Responses

  1. First – http://en.wikipedia.org/wiki/Arrows_theorem

    Second – The assmption that the groups or individuals vote randomly and independently is a very big one…

  2. A nice article on slashdot about this issue, fair voting systems etc.

    http://science.slashdot.org/article.pl?sid=08/01/06/0649217

    K

  3. A nice article on slashdot about this issue, fair voting systems etc.

    http://science.slashdot.org/article.pl?sid=08/01/06/0649217

    K

  4. […] https://kedarsoman.wordpress.com/2007/05/27/mathematical-simulation-of-election-in-democracy-india-an… […]

  5. “This is how USA democracy system works. In USA democracy, each state gets some particular number of seats in senate. California has (I think) 51 seats. So if a candidate wins 26 seats in California, all 51 seats are awarded to the candidate, thus creating a special interest group. Thus even a smaller state a bunch of senate seats, so cannot be ignored by a presidential candidate.”

    Wtf are you talking about??!!
    US Congress is comprised of the Senate, the upper house (each state having 2 Senators) and the House of Representatives, the lower house (dependent on the population of the particular state). The Senate elects the President only in the case that no one candidate has secured a majority of votes in the Presidential election and in this case each State has one vote.
    And how in God’s name can a candidate win 26 seats and be awarded 51 seats after that?? Even if he is a fat-ass redneck…how the f**k can he sit on 51 seats at the same time????? LOL!!!
    Dude, update your politics.

  6. Hey Merck,

    I am talking about the electoral vote here, for presidential election. Indeed I need to revise this as there are mistakes in description.

    However I am more interested in maths and I think the maths part is still correct.

    I appreciate you pointing out the mistake. But I would appreciate even more if you could just stick to pointing the facts and could use little more polite language.

    I am talking about maths. That’s what I wish to stick to. And considering that I am not a USA citizen and I think it’s OK if I make mistakes while describing USA political system.

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