What is pure expectancy (expectation) theory?
There is some ambiguity in your question. You ask about "pure" expectancy theory, which relates to motivation behind actions and might be categorized as a legal concept, yet your Topic selection relates to investing. Assuming that your question relates to microeconomics and investing, I'll provide an answer relevant to investment expectation theory and contrast it with motivational expectancy theory.
Investment expectation theory relates to investing in the debt market also called the bond market. The expectation theory relates to expectation of bond yields over time. This theory is controversial as the predicted results of the theory do not match the real-world outcome of bond investment results.
Critics of expectation theory posit that the reason for its real-world returns failure is that it assumes investors in the bond market are interested only in yield on bond investments. Critics further posit that investors are, in fact, interested in both maturity and yield. This position is put forth by the competing theory of "habitat theory."
Investment expectation theory holds that short-term bond market interest rates can be predicted by long-term bond market interest rates. It further holds that investing in a two-year bond would gain no more advantage in returns results than investing in consecutive one-year bonds. Expectation theory postulates that (1) since long-term interest rates (e.g., two-year bond) predict or foretell short-term interest rates (e.g., one-year bond) and that (2) since investor motivation and investor interest lies exclusively with yield on bond investments and that (3) consecutive one-year bond roll-overs are predicted to yield the same as a single two-year bond investment, then the investor can expect to be benefited by consecutive short-term investments, thus taking advantage of unpredicted rises in interest and thus hedging against unpredicted falls in interest rates.
Aside from the habitat theory criticism already noted, bond investment expectation theory seems to also hold internal contradiction, namely the contradiction between (a) the expectation of long-term interest rates predicting short-term rates versus (b) the hedging function of short-term roll-overs: if a return is truly predicted, a hedging function (though wise) is not required.
Motivational "expectancy theory" differs from investment expectation theory in that motivational expectancy theory asserts a motivational impetus (i.e., source of action) based upon a hope or unstated promise of a future action or good occurring. In law, a common example of expectancy theory describes how it is often applied to heirs named (or not named) in a will: though there is no firm commitment made to the delivery of future good, the heirs have an expectation of good based upon present circumstances. The expectancy is not rooted in vested commitment because circumstances can change resulting in change(s) to the expected terms of the will, potentially even right up until the day of death.
Though there are similarities between bond investment expectation and motivational expectancy theories, which are based upon the nature of expectation, there are significant differences. The primary difference being, of course, the concrete application of one to real-world investment and investment returns versus the theoretical hope of material future good based upon hypothetical and changeable life circumstances. These two theoretical applications of expectancy are very different theories in material terms, one having near-immediate material results versus hypothetical potential material results in an ill-defined future.
A good summary of expectancy theory is that the motivation to do something is based on the desirability of the expected outcome. More formally, motivational force (MF) = Expectancy * Instrumentality * Valence.
Expectancy- the probability that the effort will yeild the expected result
Instrumentality- the probability that the expected result is desirable
Valence- the personal value of the reward
If I work harder, will my plant produce more? -Expectancy
If the plant produces more, will I make more money?- Instrumentality
Is it worth it to me to work harder so the plant produces more?- Valence
Importantly, the motivation to pursue a course of action is not solely dependant on the outcome. Other factors play into decision-making.