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Multi-Criteria Decision Making and Exasol’s Skyline Set Function

The story of Multi-Criteria Decision Making and Exasol’s Skyline function

Most decisions made by computer are pretty dull. There’s a function for calculating a “score” for each possibility based on weighting the things you care about and the computer picks the option with the highest score.

All the really important decisions in life (and in business) are too important and too complex to be left to a computer.

That’s because all the really interesting decisions in life (and in business) have more than one dimension of “goodness”.

For example, sports have risk and they have fun – unfortunately the lowest risk sports aren’t usually much fun …

There is no mathematical way of calculating a “score” for a sport based on risk and fun – the weightings for each element will change based on whether you are in the mood for golf or ice hockey.

Similarly, with investment decisions, sometimes you are in the mood to take a punt on a dotcom stock and sometimes you want to hide your money in your mattress. One thing is universally true though: you will only take a risk if you can get a better return than for all other options of a lower risk.

This is the essence of a technique called Iterated elimination of dominated strategies (IEDS), where you remove the choices that are worse in all ways than some other choice.

This leaves you with the all sets of choices that are not “dominated” by another choice, which we call “Skyline sets”. All of these choices have an optimal combination of risk and fun and so are worth investigating in more detail.

Some (usually Americans) say that this approach was invented by Benjamin Franklin, who, when presented with a difficult decision, would write the arguments for and against on opposite sides of a piece of paper and then cross out the arguments on both sides that were of approximately equal “value”. He would then be able to concentrate on the issues that could not be crossed out.

Pareto (the same guy who invented the “80:20” analysis) discovered the basic mathematics around a century ago, but this field only really caught fire with the invention of the computer.

Unfortunately, until now there has not been an efficient method for calculating the Skyline set when there are billions of choices and many dimensions of choice. For example in standard SQL you end up with a complex “WHERE NOT EXISTS …” piece of logic that does not run well on any SQL database.

Our breakthrough was achieved through a collaboration between our R&D department and German universities. We discovered an efficient algorithm for calculating the Skyline set that could be parallelised across the Exasol database and run in-memory.

This is our Skyline function, which is new and exclusive to ExaSolution v5. To use it, all you need to do is to add a line to the SQL statement – e.g. “PREFERRING HIGH FUN AND LOW RISK” – and you get the Skyline set of choices that meet your other requirements.

From then on, it’s pretty much up to you to make the choice.

After all, no computer can tell you to play golf if you’d rather play ice hockey.


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