A group of male friends wishes to elect a “group leader,” defined as the individual whom all others must follow for the day. Each friend casts exactly two vote for another member of the group. The election proceeds as follows:

  • The individual receiving the highest number of votes is declared the winner.
  • In the event of a tie, compare their clustering coefficients. The tied candidate with the smaller clustering coefficient is declared the winner, on the reasoning that if their supporters are not connected to one another, their “loyalty” is more securely independent.

Although votes are inherently directed, the group mistakenly treated votes as a single undirected connection. Given the voting graph below, determine the winner of this entirely serious democratic exercise.

The winner is:

A. Don

B. Bob

C. Matt

D. Neal

E. None of the above

Location: São Paulo, SP, Brasil

Comments

  1. Joao MeidanisMarch 7, 2026 at 10:33 PM

    Nice question. However, no choice of edge orientations will result in out-degree 2 for every node. Since we have 10 edges, the sum of all out-degrees will be 10, but we need it to be 12 if we want out-degree 2 for the 6 nodes.

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    Replies
    1. Quiz - MO412 - Matheus RufinoMarch 8, 2026 at 1:40 AM

      It is designed in a way that if one of them voted for each other, because this is not a directed graph, there is only one link. That way, they won't all have the same amount of links so we can have a winner. Sorry it wss not clearly clarified.

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