Back to 11.1 Voting Methods

11.1 Exercise 5

Avg difficulty 2.5

A condominium association elects a new president every two years by a two-round system of voting. If none of the candidates receive a majority, the association charter states that the top two candidates will be eligible to participate in a runoff election. In a particular year, five residents were nominated. The results of the first round are given in the table below.

Candidate Votes in First Round
Abou 18
Baiocchi 10
Campana 5
Dali 11
Eugene 4
  1. Is there a winner based on the first round? Why or why not?
  2. If there is a winner, who won? If there should be a runoff, who will advance to the second round?

OpenStax Contemporary Mathematics, 11.1 Voting Methods, exercise 5

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Adapted from Contemporary Mathematics © 2023 Rice University. Licensed under CC BY 4.0. Source: Contemporary Mathematics. Imported at revision fa7c1a1.