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Optimal social well-fair is the key.

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I still like that 4 minimises poor outcomes but it looks as though 2 balances this with maximising good outcomes

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Makes housing more equitable since it somewhat corrects for the worst off.

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Achieves equity

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Algorithm 3 maximises the overall welfare, what is in my opinion the most important thing.

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Helps all but maximises the disadvantaged

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It seems fairer 4 all

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because 2 guarantees 70% of the optimum social welfare, but at the same time maximizes the utility of the worst off, which ensures a fairness in the society.

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It is the fact that bias is towards the poorest in society. At 70% . This can only benefit the whole of society representing better outcomes in the future and the encouragement of a more balanced society.

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I have not changed my choice but my reasons have been clarified. Algorithm 3 maximises overall social welfare, and this seems a reasonably fair way to deal with housing. However, I do think housing is one of the topics where specific cases need to be looked at in more detail. Does someone want an extra bedroom for their shoe collection or so the twin boys don't have to share a room with one of their sisters?

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The benefit to the poorest/lowest group in this option swayed by selection. This way the worst off benefits most, society could benefit more as other negative societal effects could be reduced. The other participants in the selection wold only be marginally impacted

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It achieves the 70% so overall outcome is as good as 1 but also protects the worse off which seems fair as protects the vulnerable population

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I switched from the 1 to 2 algorithm, because it is what I think is fairest given that it guarantees well-being by 70% and at the same time maximizes the individual utility of those who are worts off.

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70% + helps disadvantaged

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I stuck with algorithm 5 since its the one that minimize the distance between each participant's utility

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Good discussion and after relooking I decided to stay with 5. As the difference in Preferences is minimized and people received something close to their desire

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I switched from 2 to 4 because 4 appears to uphold the perception of fairness more so than 2 .

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I usually think about the benefits for society in general over one specific individual. I think that those who are worst off should be considered "special cases" and threated with a separate system especially since it's not because one is worse off that multiple others are not in need but a bit better off than that person.

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Always important to help those who need it most, algorithm 2 allows for those who receive the worst outcome still receive a baseline result.

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Welfare has as target to help and support expecially people who are in the worst condition and algorithm 2 could guarantee this result

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The best case scenario is everyone gets exactly what they want. If this is not possible then Algorithm 2 seems to be optimum as it has the possibility to guarantee 70% of social welfare to everyone and also takes care of the most disadvantaged.

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I was thinking between algorithm 2 and 4. In the first one we guarantee social welfare, but the latter one seems to be more equilibrated, trying to maximize the minimum for everyone.

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The maximin criteria ensures even the worst off have the highest possible value, as well as trying to guarantee 70% is the best way to ensure the max amount of welfare is distributed.

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Levelling up the worst off while trying to optimise welfare seems like a good solution.

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Minimising the pairwise distance between each person's individual utility while guaranteeing 70% of the social welfare seems to be a good balance between equitably distributing resources and ensuring no one is left out in the cold entirely.

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When maximizing social welfare is used as the decision metric, then it seems like individual choice is forfeited for the common good. Algorithm 5 appears to take individual preferences into consideration so that in the long run, more people will receive something that is closer to their preference (e.g. a two bedroom instead of a three bedroom).

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I agree with Rawls that it seems just to maximise the utility of the participant who is worst off, implementing positive bias to ensure that the most disadvantaged receive the optimal that can be given. A guarantee of 70% of the optimal welfare also seems to be a good proportion of welfare.