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2 and 4 are so similar that its hard to distinguish particular bias. in both cases, a similar number got a worse or better result than those who got what they wanted.  algorithm 5 has lots of people getting what they want - which given the distribution is a lower expectation of 5 - but an smaller number didnt get what they wanted.(similar for 1). 3 has some people getting way worse than what they wanted

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With the fourth algorithms, people seems to have the best outcome for them and a big majority of them seems happy

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Normally distributed distance from mean, means most people are likely to get similar outcome, even its not the one they wanted

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Based on the distribution of the results, seems most of the times and people reach a common choice.

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I sought the most optimum outcome for all.

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Because a) No one gets lower than a '2' pick b) Most people get a 5, 6 or 7 . However, it does make me wonder, mathematically speaking, how one unhappy person is weighted against the group. For example, in my assessment of 'fairness', I decided that if anyone was allocated below a '3' then that was not fair, even though mathematically, it may turn out to be so.

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Utility obtained for Algorithm 4 has lowest deviation from the mean; to me that means more people got the houses they wanted.

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I thought this appeared most fair as there was not much variance among all dwellers from the average utility level. Additionally there was not an abundance of them at the highest utility level that others would be envious of.

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Though it reaches a similar outcome for the community it drives better satisfaction at the individual level + it has a fairly narrow distribution which seems to mean that no one is truly negatively affected and there's a reasonable level of fairness.

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Algorthyms 1&5 give a fairer ditribution, although i agree with Algo 1 in that 5 has a lower number of participants that have been assigned their first choice.

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Algorthyms 1&5 give a fairer ditribution, although i agree with Algo 1 in that 5 has a lower number of participants that have been assigned their first choice.

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Algorithm 1 appears to be the fairest, as it has the narrowest distribution (like algo 5), but is better than 5 as it has a higher number of participants which have reached a utility value of 5 or greater, and doesn't have any participants which are assigned to a property below a utility of 3. Although the outcome is harsher on those in brackets 3 and 4, as the distribution overall is more equal, it is 'fairer'.

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Algorithms 1 and 5 have the narrowest distributions, showing the most "fair" allocations even though there won't be as many thrilled people with their first choice home as with algorithms 2, 3, or 4.

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Even though it doesn't distribute as evenly as #5 on graphic 2, the agregated sum of the 3 centered bars are extremely high. And when analysed graphic one alone, its by fair the fairest when meeting the bidders interest.

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The algorithm 5 seems to have a reasonable dispersion around allocation of the utilities. I suspect there is marginal benefit to the more disadvantaged consistent with John Rawls approach

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Algorithms 1&5 seem to "level down", in that the most common utility is only 5. So they are only fair in the sense that everyone is equally unhappy. Of those that "level up" to the most common utility being 7, number 3 ends up with a small number of people doing much less well ("unfair"). Numbers 2&4 appear, by eye, to disappoint in about the same pattern (though almost everyone is better off than in 1 or 5), and 4 seems to delight slightly more

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