Final answer:
In plurality voting, the pizza choice with the most first-choice votes wins, while in ranked choice voting, it involves an elimination process until one choice has a majority. The cyclical majority issue shows how choice presentation can influence decisions, mimicking sales tactics. Specific vote counts would be needed to determine the outcome for both voting methods.
Step-by-step explanation:
The student is asking how a group of 12 students will make a decision using plurality voting or ranked choice voting when selecting among sausage (S), mushroom (M), and beef (B) pizza. In plurality voting, the option with the most first-choice votes wins, regardless of the subsequent rankings. Using the ranked choice system, also known as instant-runoff voting, if no option gets a majority of first-choice votes, the option with the fewest first-choice votes is eliminated, and those votes are redistributed according to the second-choice preferences, in a process that continues until one option has a majority.Based on the information provided, if the students were comparing the three options in pairs (e.g., S vs. M, M vs. B, B vs. S), the preferences could create a 'cyclical majority', where no single option is the overall winner. Such a situation shows the complexity of the decision-making process and how presenting choices in different formats can greatly influence the decision made, echoing the insights provided by car salespeople about choice presentation.It cannot be determined which pizza the group will choose based on the information given—it would require specific individual rankings for each pizza type to apply both plurality voting and ranked choice voting methods and to identify the main answer. Still, this explanation provides an understanding of why the majority view may not always win and how the voting system used influences the final decision.