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In the context of election methods, the Irrelevant Alternatives Criterion (IAC) is a principle that expects the outcome of an election to remain consistent even if a non-winning candidate is removed from the race. It is saying that the winner shouldn't change due to the presence or absence of candidates who weren't winning in the first place.

Consider an election where we have three candidates and the preferences of the electorate are split between them. Under the IAC, if the candidate who is currently losing were to suddenly drop out, the voters who supported the removed candidate would likely redistribute their votes among the remaining candidates. Despite this redistribution, the IAC maintains that the original winner should still come out on top. In the event that the initial winner does not win after the redistribution of votes, the voting system violates the IAC.

This criterion is crucial because it measures the degree to which a voting method is invulnerable to changes in voters' preferences regarding non-winning alternatives. In simple terms, if your favorite ice cream flavor isn't available, choosing a backup flavor shouldn't change the bestseller status of the most popular flavor in the shop.

Voting theory, also known as social choice theory, examines the various methods and principles behind casting and counting votes to achieve a collective decision. It looks at the technical aspects of what makes a good voting procedure and the social implications they may have.

Voting theory addresses questions like: How can we aggregate individual preferences into a collective decision? What makes an election method fair or effective? And, how can strategic voting change an election outcome? It's about examining the strengths and weaknesses of different election methods from both mathematical and ethical perspectives. This field uses tools from economics, political science, psychology, and mathematics to understand how to best organize voting and the implications of different voting methods on election outcomes.

Election methods are the concrete systems used to translate individual votes into a group decision or the election of a candidate. There are various methods, from the widely known plurality (first-past-the-post) system, where the candidate with the most votes wins, to ranked-choice or preferential systems where voters can list candidates in order of preference.

Choosing an election method is not merely a technical decision; it involves value judgments about what aspects of democracy are most important. Some methods, like the majority system, require a candidate to gain more than half of the votes to win, reducing the chances of a winner disliked by a majority. In contrast, the plurality system allows for winners without a majority, which can lead to outcomes where the elected official does not represent the preference of most voters.

Improving the understanding of these methods can help ensure that the chosen system aligns closely with the values and objectives of the company, community, or country in question. For educational purposes, exposing students to different election methods and their implications can lead to a deeper understanding of the democratic process and encourage informed participation.