An algorithmic approach to detect non-injectivity of the Partial Borda Count

Voting is how we elect today’s voices, faces, and leaders in our country. It is argued to be a very essential right we have as a people. A voter votes, by listing their preferences. Their preferences are relating the candidates to one each other (i.e. whether they prefer candidate A to candidate B or if they are indifferent between the two). There are many different social choice functions that can be used to calculate the results of an election. This project glances over the theory of Condorcet, Borda, Arrow, and Young, all of whom had a great impact on voting theory and social choice theory. I experiment with partially-ordered preferences using the Partial Borda Count. The Partial Borda Count switches from being injective (one-to-one) to non-injective (multiple posets going to the same score vector) for all elections with 5-elements or higher. I created an algorithm that determines certain posets that go to the same score vectors for n-candidate elections (if n \u3e 5). My algorithm was able to detect all of the failures of injectivity for a 5-candidate election. I then use this algorithm to see if I can predict which posets go to the same score vector, for a 6-candidate election, without having to construct a 6-element database. It turns out my algorithm proved successful in locating some of the injectivity failures of 6-element elections