Final answer:
The Borda count and Coombs system are vulnerable to manipulability, where voters strategically misrepresent their preferences to achieve a more favorable outcome. The Borda count system assigns points to each candidate based on their rank, but voters can manipulate the outcome by strategically ranking candidates. The Coombs system eliminates candidates, but voters can manipulate the outcome by ranking their least preferred candidate higher.
Step-by-step explanation:
Manipulability refers to the vulnerability of a voting system to strategic behavior, where voters strategically misrepresent their true preferences in order to achieve a more favorable outcome. The Borda count is a voting system that assigns points to each candidate based on their rank in each voter's preference list. However, it is susceptible to manipulation because strategic voters can strategically rank candidates lower to ensure their preferred candidate does not win. For example, if there are three candidates A, B, and C, a voter may rank their true preference as A > B > C, but they can manipulate the outcome by ranking their preference as C > A > B, which may result in candidate B winning.
The Coombs system is another voting system that eliminates the least preferred candidate in each round until one candidate remains. However, this system also has manipulability concerns. For instance, voters can strategically rank their least preferred candidate higher to force the elimination of other candidates they dislike, leading to a more favorable outcome for their preferred candidate.