Final answer:
The alternatives to a 'first past the post' system that might reduce the problem of voting cycles are ranked-choice voting, open primaries, and direct democracy.
Step-by-step explanation:
Ranked-choice voting is one alternative to a 'first past the post' system that can reduce the problem of voting cycles. It allows voters to rank candidates in order of preference, and if no candidate receives a majority of first-place votes, the last-place candidate is eliminated, and their votes are redistributed to the remaining candidates based on the voters' second choices.
Open primaries is another alternative that can reduce voting cycles. In an open primary, voters, regardless of their political affiliation, can participate in the primary election and choose a candidate from any party.
Direct democracy is not specifically an alternative to a 'first past the post' system, but it is a different approach to decision-making in which citizens directly participate in making important decisions without elected representatives.