The answer is: [A]: run.
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The answer:
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Fat is to eating as elected is to run.
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Explanation:
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Think of the relationship between "eating" and "fat"; and "fat" and eating".
On a rudimentary level, fat people tend to "eat more"; and "eating more" tends to make one "fat"
So, doing something (verb or gerund) tends to result in a "one word outcome"; and all the answer choices given are "one word". As such, it makes sense that "run" is the best answer.
Also, if one "runs", then one have a tendency to get "elected".
Answer choice "A: run" is the only answer choice that makes sense.