What are some alternatives to a "first past the post" system that might reduce the problem of voting cycles?

In ranked-choice voting, also known as preferential voting or single transferable vote, voters rank candidates in order of preference, instead of voting for just one candidate. If a candidate receives more than half of the first-choice preferences, then that candidate wins. If there's no clear winner, the candidate with the least first-choice preferences is eliminated, and the votes are redistributed according to the voters' subsequent preferences. This process is repeated until a candidate wins with the majority of votes.

Approval voting is another alternative to FPTP. In this system, instead of choosing only one candidate, voters can approve or disapprove of as many candidates as they wish. The candidate with the highest approval rating (i.e., the difference between the number of voters who approved them and the number who disapproved) wins the election. Approval voting allows voters to express their preferences for multiple candidates and can reduce the chances of a voting cycle occurring.

The Condorcet method is based on the idea of pairwise comparisons between all candidates. In this system, voters rank candidates in order of preference. Every candidate is then compared head-to-head with every other candidate, and the candidate who wins the most pairwise comparisons (i.e., the candidate who would win in a one-on-one race against all other candidates) is declared the overall winner. This method tends to promote consensus candidates, as they must perform well in each of the pairwise comparisons to win the election, thus reducing the likelihood of voting cycles.

The Borda Count is a points-based voting system where voters rank candidates in order of preference. Each ranking position is assigned a certain number of points, typically with the highest-ranked candidate receiving the most points and subsequent positions receiving fewer points. After all votes have been cast, the points for each candidate are summed, and the candidate with the highest total is declared the winner. The Borda Count encourages voters to consider their preferences for all candidates, making it less likely for voting cycles to occur. Overall, there is no perfect voting system, and each alternative has its advantages and disadvantages. However, these alternatives to the "first past the post" system have the potential to reduce the problem of voting cycles and provide a more accurate representation of voter preferences.