Statistics of cumulative voting

[nomadreid]

(Disclaimer: this is a mathematics question, not a social science question)
It is not clear to me, given Arrow's impossibility theorem, why the most common forms of cumulative voting -- range, rank, and approval voting -- are advantageous over choice voting systems, such as elimination run-offs till a majority is reached, or even plurality-wins. As I understand it, cumulative voting systems are supposed to reduce the probability of vote dispersal (similar candidates splitting the bloc vote), but I do not see why. I am looking at it from a strictly mathematical viewpoint, so any answer should not bring in extraneous social considerations. Thanks.

 

[Valkarie]

The key difference between cumulative voting and choice voting systems is that cumulative voting allows for more expressive voting. In a cumulative voting system, each voter can express their preferences more precisely by distributing their votes among the different candidates. This can be beneficial in situations where there is a large number of similar candidates or when the result is expected to be close.In contrast, with choice voting systems, such as elimination run-offs, each voter can only express their preference for one candidate at a time. This limits the voter's ability to express their preferences accurately and thus increases the likelihood of vote dispersal. In addition, cumulative voting also allows for more nuanced outcomes compared to choice voting systems, which can lead to more representative results. A cumulative voting system allows for more than two outcomes whereas a choice voting system typically only has two possible outcomes (i.e. the winner and the loser). This can be beneficial in situations where there is a large number of candidates and a strong majority is not expected.