For example, an electrical company pressuring the government to vote against a political proposal that should tax this very same company.
In what way do political parties gain with the pressure of lobbies and vice versa.
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Lobbies have various ways to influence politicians in ways which are beneficial for both sides:
This answer will deal with rules specific to the United States. Other countries have different details, but many of the patterns may be similar. Or not.
Lobbyists may make donations. Of course, they are limited for individuals in the US to $2700 per candidate per election per individual.
Lobbyists may operate PACs. They can only donate $5000 per PAC per calendar year per individual, and each PAC may only donate $5000 per candidate per election year.
Lobbyists may donate money to party committees. Annually, $33,900 for the national committee and $10,000 for the state (usually combined with the local committees, as they aren't independent of the state).
Lobbyists may collect individual contributions from employees of their clients (or stockholders) and forward them to parties and candidates. The aboveboard way to do this is to have a gathering (dinner party, etc.) where they list the candidates and organizations to whom to donate. People can then voluntarily choose to write checks.
Less aboveboard, a company that gives bonuses can use the donations (large ones are reported publicly) to determine how much bonus to pay each employee. Of course, this is illegal, so they can't actually say this. Or they can use donations to determine who to promote. Again illegal but hard to catch. Did Goldman Sachs endorse Hillary Clinton? Or was she just popular with that group of people?
If the lobbyist collects the checks and forward them appropriately, this is called bundling. The lobbyists bundle the checks together so that they can say something like, "Here's $54,000 from people that want you to support the fossil fuel lobby." Otherwise, this is just a form of endorsement.
Bribes are of course illegal. The problem is that it is really hard to prove bribery. It's not enough to prove that person A gave money to politician B. That can be done legally. It's not enough to prove that politician B did something for person A. That can be done legally, particularly if A is a constituent. It's not enough to prove that A paid B and B did a favor for A. You have to prove that the reason why B did a favor for A was that A paid B.
To give you an idea of what's required, look at Bill Jefferson. They recorded him agreeing to take money in return for help getting a product purchased by the Defense Department and several foreign countries. Without that recording, even the $90,000 in cash hidden in his freezer might not have gotten him convicted.
Bribery is ultimately unnecessary. Bundling has much the same effect and is legal. They can't say, "We're only giving you this money if you agree to vote our way on this bill." But they can say things like, "We've been big supporters in the past. Don't expect that to continue unless you vote our way on this bill." Or "We're planning our political donations now, and we like yes on this bill." Most politicians would get the message.
Despite the name, a "SuperPAC" isn't actually a PAC but a type of nonprofit. These organizations may spend an unlimited amount on advertising or other electioneering activities favoring a candidate or party. They may receive unlimited anonymous donations from individuals and corporations (individual states may require donor identification but the federal government does not). They may not donate anything directly to candidates and parties and they aren't allowed to coordinate with candidates or parties. This makes them hard for lobbyists to operate (the whole point of a lobbyist is to coordinate legislative activity with politicians), but these are constantly in the news.