Is There a Dictatorial Ranking Factor in Search Engine?

The famous economic theory named "Arrow's paradox" may indicate that there is a dictatorial ranking factor for search engines

Posted by Ryan on 2012-05-30

Recently I happened to read about a famous economic theory named “Arrow’s paradox“, and inevitably related it to search engines.

Quoted from Wiki:

The framework for Arrow’s theorem assumes that we need to extract a preference order on a given set of options (outcomes). Each individual in the society (or equivalently, each decision criterion) gives a particular order of preferences on the set of outcomes. We are searching for a preferential voting system, called a social welfare function (preference aggregation rule), which transforms the set of preferences (profile of preferences) into a single global societal preference order. The theorem considers the following properties, assumed to be reasonable requirements of a fair voting method:

1. Non-dictatorship

The social welfare function should account for the wishes of multiple voters. It cannot simply mimic the preferences of a single voter.

2. Unrestricted domain

(or universality) For any set of individual voter preferences, the social welfare function should yield a unique and complete ranking of societal choices. Thus:

It must do so in a manner that results in a complete ranking of preferences for society.
It must deterministically provide the same ranking each time voters’ preferences are presented the same way.

3. Independence of irrelevant alternatives (IIA)

The social preference between x and y should depend only on the individual preferences between x and y (Pairwise Independence). More generally, changes in individuals’ rankings of irrelevant alternatives (ones outside a certain subset) should have no impact on the societal ranking of the subset. (See Remarks below.)”

I personally interpreted the three statements from the perspective of search engines as follows:

  1. if all ranking factors of a search engine rank Page A before Page B, then in the final search engine results, Page A has a better ranking over Page B (Unrestricted domain);
  2. No single ranking factor can ultimately determine the final ranking order of a set of web pages, regardless of ranking orders determined by other ranking factors (Non-dictatorship);
  3. If the ranking orders of A and B determined by all the ranking factors are unchanged, then the final ranking order of A and B is unchanged. We can consider this as a political campaign – say in the first round of voting, Candidate A beats Candidate B, then in the second round of voting, if all the voters don’t change their preferences between A and B, Candidate A will still beat Candidate B, with or without new candidates added, removed etc ((IIA))

The interesting part is the conclusion of Arrow’s paradox is that the three statements above can not be all true at the same time (Mathematical proofs can be found on the Wiki page ).

If Statement 1 and 3 are true, then Statement 2 is false, which means there is a dictatorial ranking factor.

Do you think there is dictatorial ranking factor? If so, what is it possibly?

Let me know your thoughts – feel free to leave a comment, drop me a line at [email protected] or join the LinkedIn discussion here

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