Fairly Distributing Undividable Goods: A Challenge

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Finding a fair algorithm for distributing undividable goods among individuals with varying preferences and priorities is complex. A proposed approach involves rating choices to maximize overall satisfaction, but details on implementing this fairly are needed. Considerations include giving priority to individuals who missed out in previous rounds. Suggestions for further research include exploring keywords related to fair division algorithms and mechanisms. The challenge lies in balancing individual preferences while ensuring equitable distribution.
Gerenuk
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Can you give me a suggestion how to find a reasonable algorithm do distribute undividable goods among different people? All of the people have different preferences, but might be clashing. Also some of them might have priorities, due to not getting anything last round.

So for one round there are objects A,B,C,... and many people how put down their individual preferences for them. Some of these people should be given a higher chance of getting one object (either in addition to the chance of getting others or just more security in getting one object at all).

A basic idea is of course to rate all choice and maximize the total number of ratings satisfied, but I don't know about details how to make this fair or clever.

Or can some suggest keywords or algorithms I should search for on the internet?
 
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