Most users are incapable of writing good Boolean Retrieval queries.

feast or famine problem

Boolean Retrieval either returns too few or too many results: AND queries return often too few results \(\min (x,y)\), and OR queries return too many results \(x+y\).

This is not a problem with Ranked Information Retrieval because a large result set doesn’t matter: top results just needs to be good results.

free text query

Instead of using a series of Boolean Retrieval, we instead give free text to the user.

rational numbers are ratios:

\begin{equation} \mathbb{Q} = \left\{\frac{a}{b} \middle| a,b\in \mathbb{Z}, b\neq 0\right\} \end{equation}

Motivation

Suppose we would like to say that “we prefer all to well \(A\) more than bad blood \(B\)”

\begin{equation} A \succ B \end{equation}

No right or wrong answers in this statement by itself, but we can check whether or not your preferences are inconsistent with itself.

von Neumann and Morgenstern Axioms

Axioms for checking if a set of preferences are rational. The axioms allow you to check if a set of decisions are Rational Preferences.

\(\mathbb{R}\) real numbers are numbers generatable by a possibly infinite sum of powers of 10.

plan to depth \(d\), take action, replan