It's only a negotiation if the official has any chance of being prosecuted for that bribe.
>> But if you have a piece of paper that says “I am so against bribery that I carry around pieces of paper that say so” it makes the cop lose hope of getting the bribe.
Or well, the cop simply arrests you and puts you in jail for a week during which you can't go to work to afford food for your children.
>> If a person is told “pay this $100 fee right now or I’ll have to take you in” and says “no”, the cop may lower the price, raise the price, threaten more, or follow through on the threat to try to get the person to pay up.
There was a thing in Russia about a decade ago for people driving cars with European plates: a cop stops you and says you're drunk. You argue with him, so he takes you to a doctor. Doctor says you're drunk.
So the bribes went as $10 for the first time and then $100 at the doctor's. If you were smart you knew you could loose the license in Russia and then simply report it stolen in Europe because nobody shared databases.
I’m not saying it’s fair, but it is a negotiation. There are offers and counteroffers that are accepted and denied.