Mankiw says no, Caplan says the real problem is voting itself. Of course we let private shareholders sell their votes all the time, and uncontroversially, so the real issue is how politics is different.
Say society has a 9999 people. The marginal private value of a (political) vote is almost zero, except for its feel-good benefit (see also Gelman on altruistic motives to motivate voting). Yet the total value of 5000 votes — a winning tally — is the size of the largest wealth transfer that the winner could impose on everyone else. The result will mimic a model of self-interested voting but with only one self-interested voter — the owner of the purchased votes — having a say. And that winner will be the conscience-less (non-liquidity-constrained) person who has the most to gain from buying up votes and getting things his way.
Of course Bryan, in other contexts, has shown that expressive voting is more likely than the self-interested voting model, at least under standard democracy. I would rather have expressive voting than what is explained directly above, even though expressive voting is somewhat irrational.
Maybe voters will end up with sudden attacks of conscientiousness and be unwilling to sell their votes; to that extent vote-selling won’t much matter and of course then it can’t bring gains either.
Now let’s go back to the corporate case. When it comes to policy, shareholders might not agree on means but everyone favors the same end of profit maximization. A winning coalition of shareholders can’t do much to extract rents from other shareholders, unless of course they are exploiting those other shareholders in their other roles as consumers or input suppliers. But such effects are usually small (as opposed to the widespread possibilities for redistribution through politics) and thus vote selling works just fine for corporations. There is no simple way that shareholder A can buy up the votes of shareholders B and C and then just screw them over.
Coda: There is a potential problem with vote-selling in corporations, again relating back to the difference between marginal and average value for a vote. Shareholders might be afraid to sell to a takeover artist, instead wishing to hold on for the ride and reap gains from the change in corporate control. But if no one sells the takeover cannot take place and no one reaps the gains. In other words, there is too little vote selling; that’s Grossman and Hart, 1980. Alex once wrote an excellent paper on this problem (but where is the link Alex?) and showed that the free-rider problem among shareholders can usually be solved by random Nash strategies; note that the final outcome will depend on whether there is a countable or uncountable infinity of shareholders; please don’t laugh!
The bottom line: There are good economic arguments for why we allow corporate vote-selling but not political vote-selling.