Here in the U.S. the notorious McCain-Feingold law is an attempt to curb this problem. It is notorious because it does so by restricting free speech. In particular, it restricts who can spend how much on what kinds of speech running up to an election. Inevitably, it and similar laws are both full of loopholes and contrary to the spirit, if not the letter, of our First Amendment.
There is a far better solution that does not have significant loopholes and does not regulate any speech: make elections unpredictable. If would-be purchasers of political favors cannot predict who will win, or even who might win with substantial probability, they cannot purchase any favors prior to an election. A perfectly unpredictable election would be bribe-free.
The Grand Council Chamber in Venice
We can't make elections perfectly unpredictable, but we can get pretty close. There are historical and even contemporary precedents. For example, we choose jurors by lot from a pool much larger than the twelve jurors selected. This prevents wealthy plaintiffs, defendants, or governments from buying jurors through the selection process. (After selection, there are a number of legal and physical sequestering mechanisms that can be used to isolate a jury from contact with favor purchasers. As for political office, this article deals only with bribery during the selection process).
In ancient Athens, not only juries but many office-holders were selected by lot. But the most intriguing unpredictable election process was probably that of the medieval Venetian Republic. This republic helped turn a secure island into Europe's wealthiest trading empire. In Venice, many political offices were selected by a repeated cycle of lottery, vote, .... lottery, vote. The final lottery and vote, at least, were held one after the other in the same room, giving favor purchasers no time or privacy to do their business. The leading office in Venice, the Doge, was selected by a Great Council of about 2,000 members from those members, through a process that can be diagrammed as follows:
2,000 --> L30 --> L9 --> E40 --> L12 --> E25 --> L9 --> E45 --> 11L --> E41 --> EDScott Gordon describes this process as follows:
L refers here to selection by lot; E to selection by election [voting]. In the Great Council, by the drawing of balls from an urn, 30 members of the Council were selected; a further drawing reduced these to 9 who met to elect 40 men. This 40 was reduced by lot to 12 who proceeded to elect 25, and so on until the final election selected 41 nominators, who submitted their choice to the Great Council [i.e. made the final vote for Doge].The process is loosely similar to the confusion/defusion cycles of encryption or the repeated mixing phases used for securely anonymous Internet communications. The Venetians alternated a randomizing step with a debate-and-voting step. It's not clear what, if any, function was served by the particular number choices or some of the other detailed structure. Each elector presumably had a substantial but fixed number of votes, so that there would exist a top 40, 25, 45, or 41 of vote getters despite being only 9, 12, 9, or 11 electors respectively.
I suggest the following leaner structure. A modern congressional election, for example, might look like this:
600,000 voters / 100 candidates --> E23 --> L7 --> E19 --> L11 --> E17 --> L7 --> E19 --> EMThus the top 23 vote-getters (by the 600,000 voters) are selected, from whom 7 are chosen by lot. These lucky candidates, who now serve as electors, then elect from among all the candidates except themselves 19 electors, who are whittled down by lot to 11. These elect 17 electors from the candidates except themselves, who are whittled down by lot to 7. These final seven then elect 19 final electors except themselves, who proceed to elect the Representative from among all the candidates except themselves.
This should probably be done online at a scheduled time, if an online election can be made secure, rather than trying to get all the elector/candidates to meet physically at one or more scheduled times. The last two steps at least need to proceed quickly enough that no deals can be done between or during them. With reliable connections and good user interface design it should go quite fast. The preceeding election steps should usually include time and communications channels for debate and research, but not enough time to forge the social relationships often necessary for reliable favor purchase.
I've used prime numbers based on a possibly superstitious analogy to the use of prime numbers in cryptography or by cicadas, i.e. on the hunch that prime numbers will make each step less predictable than with factorable numbers. The process of signing up to be a candidate must be very easy, so that we can get large numbers of people signing up to run in even small elections. The fact that they double as both electors and candidates who might get elected to office increases the motivation to become an elector/candidate. A further benefit is that electors, themselves elected, can prevent a demagogue from being chosen, while the election cycles make it less likely than in a pure lottery for a whacko or incompetent to be chosen.