With Election Season in full swing on the campus, it is an
opportune moment to quickly go over how Game Theory is applied to Politics.
The Simplified
Setup
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Two parties - Congress and BJP which have to decide on
their “ideologies”
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Ideologies are represented on a scale 1 to 10, where
the smaller a number, the more orthodox Congress-ideals there are; and larger a
number, the more orthodox BJP-esque the ideologies are
●
There are 10 states with equal population that
correspond to each of these numbered ideologies.
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The two parties will choose a “position” for their
campaigning on the “political spectrum” of 1 to 10
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Each state will vote entirely for the party closest to
them. In case of a tie, the voters split evenly.
●
Therefore, in this game:
○
Players = 2 political parties
○
Payoffs = Maximizing their %share of votes
○
Strategy = Choosing the correct political position
Step 1: Identifying
the Dominated Strategy
It is probably intuitive that both positions 1 and 10 are
dominated strategies, i.e, if Congress were to choose position 1, then
regardless of what position BJP chooses (except 1 or 10), it’ll be better off
than Congress.
For example, suppose, Congress chooses position 1, and BJP
chooses position 7. Then, the votes will split (depending upon distance) as
follows:
Positions 1, 2, 3 are closer to Congress than BJP; therefore
they all vote for Congress.
Positions 5, 6, 7, 8, 9, 10 are closer to BJP than Congress;
therefore they all vote for BJP.
Position 4 is equidistant (between 1 and 7). Therefore, the
vote there is split.
Similar iterations for all positions against 1 will show
that position 1 will always lose.
Similarly, position 10 will always lose.
Therefore, these are the dominated strategies. (In this
case, they are strictly dominated)
Step 2:
Simplifying the Game
Now, assuming, rational players, no one will choose
positions 1 or 10. These dominated strategies are therefore taken out of the
game and with the remaining choices, the game now becomes:
Step 3: Iteration
Using the same arguments, it is clear that positions 2 and 9
will be the dominated strategies this time. And therefore they will be struck
off from the game - eventually leading to only two positions remaining - 5 and
6, in which case the voters are divided equally, 50% each.
Thus, both BJP and Congress will be forced to take up
positions very close to each other. This is one of the reasons to why most
political parties often seem the same to us, and why on most issues it is
advantageous or profitable to take the most “diplomatic” stance possible. A
similar strategy, some argue, is also being used by Modi - where is balancing
“development” and “Hindutva”.
This framework is called the Median Voter Theorem.
Limitations:
●
Voters are not evenly distributed
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Not every votes; voter turnout needs to be taken into
account
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The strategies will change with increase in the number
of players, i.e., if more parties contest elections.
●
Just because the party positions itself at 5 or 6,
doesn’t mean the people will believe them
