Favoritism, or favoing, is a method of trolling players in Transformice, letting a specific mouse be the first mouse to enter the mouse hole for their "Cheese gathered first" stat to increase, as well as them getting more points. Sometimes, a shaman will only let this one specific person enter the hole and nobody else, and the shaman may kill the other mice.
The more passive way of favoing is when the shaman only helps one specific person get first, be it their friend, somebody they have discussed this with, or to a lesser extent a random player (as a form of trolling), and then helping the other mice afterwards.
A good way to prevent favoing players and their friends is to try to make them leave the room by trolling them back or sending non-offending, but raging messages, though these methods almost never work for mice and rarely even lead to you being vote-banned or muted. Generally, mice and moderators are harmless against favoriters because they are strict with rules, except for trapping mice what sometimes lead to ban.
Ways to favo include attaching a balloon to the specific mouse, teleporting them, and letting them get the cheese, kill themselves, and then reviving them using the Ambulance skill while standing on top of or near the hole.
It can be used as a trolling method if the shaman kills all the mice and only values one mouse, or favos with the intentions of annoying people rather than letting this person have first.
Sometimes shamans will favo random people, people with whom they have not discussed this matter beforehand, in order to prevent stat padders from succeeding, or make other mice mad and ruin their chance of getting firsts.