## 1. Different Voting Methods

In one electoral district, 100,000 voters are casting their votes. Three candidates are running: Montoran, Ajuda-Pinto, and the Usselian vidam ${ }^{1}$.

The residents of the district are divided into four groups, each of which evaluates the proposed candidates differently.

The first group, consisting of 33,000 voters, prefers Montoran over the other two candidates, followed by Ajuda-Pinto, and the Usselian vidam is last.

The second group, including 18,000 voters, favors Ajuda-Pinto, followed by Montoran, with the Usselian vidam still in last place.

The third group, comprising 12,000 voters, prefers Ajuda-Pinto, followed by the Usselian vidam, and finally Montoran.

The fourth group of voters, consisting of 37,000 voters, prefers the Usselian vidam; followed by Ajuda-Pinto, and Montoran is last.

Which candidate will be elected?

Consider three different voting systems:
1. If the election is held in one round, Montoran will receive 33,000 votes, Ajuda-Pinto - 30,000, and the Ussel warden - 37,000 votes. Therefore, the Ussel warden will be elected.

In a two-round election, the two candidates who receive the most votes in the first round will compete, i.e., the Ussel warden and Montoran. The latter will receive 51,000 votes ($33,000 + 18,000$), while the Ussel warden will receive only 49,000 votes ($12,000 + 37,000$). Therefore, Montoran will be elected.

In a three-round election, the "duel" between Montoran and Ajuda-Pinto is won by Ajuda-Pinto with a score of 67,000 votes against 33,000; the "duel" between Ajuda-Pinto and the Ussel warden is again won by Ajuda-Pinto, this time with a score of 63,000 against 37,000. Finally, the "duel" between the Ussel warden and Montoran is won by Montoran with a score of 51,000 votes against 49,000.

According to the results of the three rounds, Ajuda-Pinto is in the lead, followed by Montoran and, finally, the Ussel warden. In other words, Ajuda-Pinto wins.

Thus, without resorting to any special methods of voter agitation - solely by choosing the voting system - one can achieve the desired election of any of the three candidates.