For your example to more accurately reflect reality, the students would vote for a representative who then decides that the class will buy caviar cookies where only one or two deviant student like and will eat. Some crumbs from the caviar cookies are then shared by the rest of the students …

Voting itself is flawed. Aristotle stated that voting leads to oligarchy rather than democracy. Democracy, he said, requires a lottery in choosing representatives. Aristotle arrived at that conclusion based on observing city-states in his time. The reason why voting is a flawed mechanism is clear. It is subject to the influence of money, cronyism, nepotism, racism, classism, sexism, incumbency, misinformation and other undesired influences. All those disappear with a random lottery. As an example, you automatically get a near 50-50 split in representation between men and women.

As for the problem of the abuse of minority, that can again be directly handled by a lottery. You first randomly choose representatives. This automatically provides an unbiased sample (in the statistical sense) of the PREFERENCES of the population. The representatives then propose or support projects according to their preferences. You then do a random weighted lottery of those projects according to the number of supporters. If you have 51 chocolate chip cookie supporters and 49 caramel cookie supporters then that’s the frequency of how you get those cookies selected. Think of a secondary lottery of 51 tickets for chocolate and 49 tickets for caramel. Ditto for a 70-30 split or any other multi-way kind of split.

Your main point is right though: Only randomness can conquer the quantization of unfairness in society.