I know I’ve already asked this, but I am curious about if you are allowed to buy votes of people who are willing to participate. Using Flashlib’s idea, what if the people voted for a party in exchange for the answer of a complex math problem and voted against themselves or sat out if they didn’t? This has to do with the 1st amendment because of the data being speech, and my guess is 18 USC 597 doesn’t apply because it is speech though i am not sure because the meaning of the word expenditure could be unclear. So, is that an expenditure?
Your premise that a solution to a math problem has no value is faulty: it is of value to some people (mathematicians), but probably not to me or most people. You can read the DoJ article on prosecution of election offenses, looking for discussions of "thing of value". Ultimately it would be up to the court to determine whether offering a thing of personal value but no general market value constitutes offering a thing of value. It seems pretty clear to me that "a thing of personal value" is "a thing of value".
You essentially ask whether such behaviour as you described would be an "expenditure" per the law. Well:
The term “expenditure” includes— (i) any purchase, payment, distribution, loan, advance, deposit, or gift of money or anything of value, made by any person for the purpose of influencing any election for Federal office; and (ii) a written contract, promise, or agreement to make an expenditure.
If the thing you describe does not have value, why would people vote for a particular party in exchange for the thing? If the thing you describe does have value, why would its exchange for votes not fall within the above definition of expenditure?