The aim of Mechanism Design is to plan or devise a mechanism that guarantees certain objectives, based on the two assumptions that agents have strategic behaviour, and that they have private information only known to them. As such, elections can be seen as an example of a democratic mechanism. In a setting where agents have a personal utility function that they want to maximize, and where they cannot be relied upon to disclose their preferences honestly, elections are a seemingly simple way of getting agents to reveal their preferences.

However, such an electoral mechanism may run into many problems. Firstly, there could be more than one equilibrium, and a mechanism designer may not know which one to expect. Second, agents could mis-coordinate, and play none of the expected equilibria. Finally, asymmetric equilibria are implausible under such a mechanism.

Leaving aside these problems and the numerous weaknesses of democracy, mechanism design can give us meaningful insights when it comes to the democratic process in a plurality voting system, especially in a country like India.

Duverger’s law, named after French Sociologist, Maurice Duverger, states that plurality rule elections, such as a relative majority voting rule, structured within single-member constituencies, tend to favour a two-party system. What this means is that plurality-rule systems, often result in having effective competition only between two viable candidates. This is because, if there exists a third candidate who has a low probability of being elected, voters are better off casting their votes for one of the two candidates who are in effective competition with each other, rather than for the third candidate.

For the purpose of illustration only, let us consider a Bayesian Game setting with an electorate of n number of voters (indexed by i), who have 1 vote each, where n is any finite number:

i = 1, 2, ……, n.

Let there be an odd number of candidates, say three – A, B, and C, such that the set of outcomes, O is:

O = {A, B, C}

For this example, we consider voters who have private values i.e., they have preferences over the candidates that are not known to the mechanism designer, or to any other voter. Knowing one’s own type however, does not tell him or her anything about the rest of society, and how it votes.

Suppose we have three types of voters, such that the set of types, Θ is:

Θ = {α, β, γ}

Where,

α types have utility 3 for A, 2 for B, 1 for C; that is, α types prefer voting for candidate A the most, followed by B, then C.

β have utility 3 for B, 2 for A, 1 for C; that is, β types prefer voting for candidate B the most, followed by A, then C.

γ have utility 3 for C, 2 for A, 1 for B; that is, γ types prefer voting for candidate C the most, followed by A, then B.

All three types get utility 0, if they vote for a candidate, and the candidate does not win the election.

Now, we assume hypothetically, that the shares of each type of voter in the population are as follows:

P(α) = 45%.

P(β) = 45%.

P(γ) = 10%.

i.e., the population of our hypothetical electorate, consists of 45% of A supporters, 45% of B supporters, and 10% of C supporters.

Under a Plurality-Rule voting mechanism, we would have a two-candidate equilibrium, where:

α types vote for A.

β types vote for B.

γ types vote for A.

Now, the question is, why do γ types vote for C? This is because, even though the γ types prefer voting for C the most, they do not do so in equilibrium, given that they only form a small proportion of the population, and hence, can never create an outcome where C wins a plurality rule election. Hence, they vote for the next best alternative to maximize their utility, i.e., by construction, they vote for candidate A (Without loss of generality, they could have voted for B too, if their preferences were constructed to prefer C the most, followed by B, then A).

In the two-candidate equilibrium, if γ types voted for C, these would have been wasted votes, as it will not have any consequence in terms of getting C elected. It is the α and the β types, by virtue of their larger population shares, who will actually determine whether A or B win.

So, in our hypothetical world, candidate A wins with a total vote share of 55%, as compared to B with a total vote share of 45%.

With the benefit of hindsight, we can apply the results of this model to a live example – The 17^{th} General Elections in Meghalaya. For simplicity, we only consider the top three candidates in each constituency, and thus, the vote share will not add up to 100%.

The following two tables have been derived from the Trivedi Centre for Political Data’s Lok Dhaba Dataset.

**Shillong:**

Candidate Name | Party | Position | Votes | Vote Share | ENOP |

Vincent H. Pala | Indian National Congress | 1 | 419689 | 53.52% | 2.38 |

Jemino Mawthoh | United Democratic Party | 2 | 267256 | 34.08% | |

Sanbor Shullai | Bharatiya Janata Party | 3 | 76683 | 9.78% |

**Tura:**

Candidate Name | Party | Position | Votes | Vote Share | ENOP |

Agatha K. Sangma | National People’s Party | 1 | 304455 | 52.22% | 2.27 |

Mukul Sangma | Indian National Congress | 2 | 240425 | 41.24% | |

Rikman G. Momin | Bharatiya Janata Party | 3 | 31707 | 5.44% |

Clearly, as can be seen from the tables above, we have only two popular candidates in each constituency, and a third unfavoured candidate who has a low probability of being elected. The vote share for the third position candidate would have been larger, had we considered a non-strategic environment where Duverger’s Law would not hold.

Now, we turn to the Effective Number of Parties (or ENOP) measure, given by *Laakso & Taagepera* (1979), as follows:

Where,

n is the number of parties with at least one vote.

p_{i} is each party’s vote share.

Clearly, when we consider ENOP, which provides for an adjusted number of political parties in a constituency’s party system, we see that the figure is approximately 2 for both constituencies, which means that essentially, true political competition is only between two parties in each constituency, which is in accordance with Duverger’s Law.

Thus, in any voting system in which Duverger’s law holds, third parties are permanently overlooked, and consequently, the electorate suffers from massively reduced voter choice, idea-deficits, and a quality deficit in governance. A proportional representation system in which divisions in an electorate are reflected proportionately in the elected body therefore, would create electoral conditions that foster the development of many parties, which would not marginalize smaller or less popular political parties.