This morning, I was having breakfast in London when I came across this Visual Capitalist post on quality of life in cities. Three of the cities I consider to be among the greatest in the world (Paris, New York, and - of course - London) came below the median on quality of life.

The post used data from Numbeo, a large and well-known source which rates and ranks about 300 cities globally. An exploratory discussion with ChatGPT confirmed that the Numbeo QoL index is a weighted sum of several sub measures (purchasing power, house price to income ratio, cost of living, safety, healthcare, commute time, pollution and climate).

This led me to the following question - Can every city be above median, given some set of (non-negative) weights? So I asked ChatGPT to work it out. Below is a substantial extract of its answer, because it illustrates not only that it could work this out, but also that it did so in an elegant and efficient manner:

On the current Numbeo table of 303 cities, the answer is surprisingly:

No. There is not a single city that is incapable of getting above the median if the eight component weights are allowed to vary freely but remain non-negative.

The result has a neat structure:

  • 302/303 cities don’t even require optimisation. Each is above the median on at least one of the eight individual dimensions. Put essentially 100% weight on that dimension, and that city is above the median overall.

  • New York is the sole exception. It is below the median on every individual component. Its best single-component rank is only 164th, on climate.

  • But New York can nevertheless get above the median by combining dimensions. For example, weighting approximately 28.5% purchasing power + 71.5% climate, with all other weights zero, puts New York at about 148th out of 303.

This is a great illustration of the arbitrariness of rankings based on weighted sums of measures - the conclusion concerning which cities are above or below average on quality of life depends entirely on the relative weight of the measures taken.

I asked ChatGPT to repeat the analysis for the 2026 Guardian league table of UK universities. It noted that the Guardian actively blocked it from downloading the data, so it asked me to do it, giving me the direct link to do so. This worked fine - it’s a publicly available file! I’m noting this only because it’s interesting that The Guardian seems to actively try to prevent AI assisted analysis of their data?

The key result is the same. To quote:

On the eight university characteristics the Guardian chooses to display, there is no university in the entire league table that must remain below median under arbitrary positive valuation of those characteristics.

So, any university can be above average, depending on what you value.

But let’s push a bit further on the data publication issue. ChatGPT could not do the full analysis it had planned because there are data used in the Guardian calculation that are not in the spreadsheet. Some of that data is not publicly available anywhere, while some of it can be approximated from HESA.

I decided to go the route ChatGPT suggested of trying to reconstruct the rankings using HESA data on student numbers, and so asked it to do this. HESA also blocks automated download of the raw data, but ChatGPT did some quite sophisticated workarounds, and reconstructed the Guardian index with a high correlation (> .9). Its description of this 20 minute piece of work is informative but quite extensive, so I’ve linked part of it here rather than quoted it.

It turns out that there are two (out of 123) universities that can’t be above average, however you (non-negative) weight the components - Roehampton and Brighton.

At the other end of the scale, Plymouth’s best possible rank is 27th (against an actual Guardian rank of 84th) and Westminster’s best possible rank is 23rd (actual: 122nd). 27 universities can be number one.

In terms of the underlying points here, I make no claim to major novelty, and below is a (ChatGPT assisted) list of some previous related work I was previoulsy unaware of because I hadn’t looked. But there are I think three points here that are worth (re-)making:

  1. League-table rankings can be enormously sensitive to the relative importance they place on their components. It is therefore important to ask who chooses the weights, how they did that, and what their goals are.

  2. In two real cases, almost anything can be above average given the right non-negative weighting, and in the one case I looked at, about 20% can be the best.

  3. ChatGPT has become a very competent analysis partner. If you’re interested, take a look at my previous post on ChaGPT from four years ago. The change is enormous. We now have a tool to support much of the heavy lifting of analysis, turning what would have been a major exercise four years ago into a casual activity done while being a bit sick with flu-like symptoms, having breakfast and getting dressed.

  1. Lorenz, J., Brauer, C. & Lorenz, D.A. (2017). “Rank-Optimal Weighting or ‘How to be Best in the OECD Better Life Index?’” Social Indicators Research, 134, 75–92.

  2. Saisana, M., Saltelli, A. & Tarantola, S. (2005). “Uncertainty and sensitivity analysis techniques as tools for the quality assessment of composite indicators.” JRSS A, 168, 307–323.

  3. Saisana, M., d’Hombres, B. & Saltelli, A. (2011). “Rickety numbers: Volatility of university rankings and policy implications.” Research Policy, 40, 165–177. P

  4. Paruolo, P., Saisana, M. & Saltelli, A. (2013). “Ratings and rankings: voodoo or science?” JRSS A, 176, 609–634.

  5. Lahdelma & Salminen’s SMAA literature, especially Lahdelma & Salminen (2001), SMAA-2: Stochastic Multicriteria Acceptability Analysis for Group Decision Making, Operations Research, 49, 444–454.