1. Politicians are bought already, and that money should go to voters instead. For all the efforts that have gone into campaign finance reform, limiting donations from lobbyists, the "toothpick rule", and so on, D.C. is still awash in political money. Revolving door jobs for Congresspeople in the industries they formerly regulated are common as well.
Lots of money is made by being in Congress, and those people hardly even need it! Average net worth for a Senator is about $14 million. Let's democratize the bribery and have some of the spoils go to the common people instead.
2. Direct transfers are better than indirect transfers. Politicians already buy votes through generous entitlements and pork barrel politics for their districts. But, as any kid will tell you, it's better to get a twenty dollar bill than a $20 gift card. People would probably prefer to get direct transfers for their vote, but because that's illegal, the second-best solution is to give lots of indirect transfers instead. These also cause distortions and economic inefficiency, which would be lessened if money was just given in lump sums to voters.
3. Improved fiscal policy. Entitlement programs like welfare, Medicare, Social Security, and so on create vested groups of voters who will vote to keep those programs around during their lifetime, even though they will likely bankrupt the next generation. This makes reform nearly impossible. But what if you could buy out senior citizens by giving them a cash transfer equivalent to their expected Social Security benefits if they vote for reform?
In effect, purchasing votes introduces Coasian bargaining to the political process, which can help reduce externalities created by majority-rule democracy. If voters choose candidates selfishly, that selfishness can be harnessed for the common good and improve public policy, leaving us all better off. When peanut and tobacco subsidies were cut a similar "buy-out" policy was used to lessen opposition from farmers, so the idea is hardly unprecedented.
4. It has a long and distinguished tradition in America. In early American history, voters were brought to the polls with offers of free food and drink. I suspect reviving this practice would lead to a great increase in voter turnout.
File this away under the "posts which guarantee I'll never have a career in politics" section.