1. Check how many people got a house with a low value (1-3). Therefore Alg. 5 is ruled out. Alg. 1, 2 and 4 are approximately equally good. Alg. 3 insignificant worse (difficult to see the exact numbers on the small graphics).

2. Check how many people got a house with a high value (5-7). Alg. 3 and 4 are best.

3. Check how many people got a house with 6-7. Alg. 3 is by far the best.

4. The distribution in relation to the average does not show any major peculiarities in Alg. 3 (only a few outliers in the negative range).

Is This Fair?

Fairness depends on the criteria used:

If fairness means equal opportunity based on purchasing power, then the system may appear fair.

If fairness means equitable distribution of housing based on need, then the observed disparities suggest potential unfairness, particularly if some groups consistently receive lower-quality housing.

While fairness is crucial in any allocation system, we cannot ignore the potential long-term consequences of inefficiency. If an algorithm only prioritises fairness without considering practical constraints, it could:

• Slow down the allocation process, leading to longer waiting times for housing.

• Miss opportunities for better matches, as rigid fairness rules might prevent people from being assigned homes they would have been happier with.

• Lack adaptability, making it harder to adjust the system as circumstances change.

Algorithm 2 offers a middle ground—it still prioritises fairness, but without forcing an unrealistic level of equality that could negatively impact the system’s effectiveness in the future. This approach allows for incremental improvements while maintaining a degree of equity in allocation.

The Political & Ethical Risks of Algorithm 3

One aspect that stood out to me is how Algorithm 3 (Red) maximises happiness for the majority but creates clear "winners" and "losers". This could be seen as the easy political choice—one that ensures most people are satisfied while ignoring those negatively impacted.

From a political perspective, it’s easy to imagine decision-makers favouring this approach because:

• It maximises positive public perception, ensuring the majority is content.

• It allows them to justify the outcome using numbers, even if some people receive significantly worse results.

• It could be used strategically before an election, where keeping the majority happy is prioritised over fairness for all.

However, this raises ethical concerns. If such a system favours privileged groups or reinforces existing inequalities, it becomes a tool for political gain rather than an equitable housing solution. A truly fair system should ensure fairness without sacrificing efficiency, while preventing exploitation for short-term political objectives.

How Do We Ensure Long-Term Fairness & Efficiency?

If Algorithm 2 presents the best balance, how do we ensure this fairness-efficiency trade-off remains in check over time?

• Should the system include adaptive learning mechanisms to adjust the balance dynamically?

• Should human oversight be required to prevent the algorithm from drifting too far towards either extreme?

• What safeguards should exist to prevent political or corporate interference in data-driven housing allocation?

I’d love to hear your thoughts:

• Do you agree that fairness alone isn’t enough if inefficiency creates long-term harm?

• Alternatively do you think a strictly fair system (Algorithm 5) is the better approach regardless of efficiency?

• This has been a great example, where I am seeing a lot of people choose Algorithm 5 or Algorithm 3....do you disagree with my thoughts on Algorithm 2 above?

Cheers,

Seamus

We've seen more people in Algorithm 2 obtain utility closest to the mean and it reflects a number of data points which would impact how the algorithm would impact the whole population. In addition more people closest to obtaining utility in both the +1 and -1 distribution.

It's been a while since I studied statistics so I am thinking Algorithm 1 could also be correct based on the highest number of people obtaining utility but when we examine the diagram on the left, more people achieved utility across their preferences from 5 to 7

The vast majority of people obtained high utility value, and although there is some significant variation on distance from mean utility, the values tend to be on the higher side, indicating that utility is actually higher for many people when it deviates.

While algorithm 5 is likely the most "fair", it has the worst utility of any of the algorithms, indicating that fairness for this model means everyone is equally unhappy.