# Does Preference have a Hierarchy? A Silly Question

I have what is probably a very silly question, but I have gone down the rabbit hole and can’t get back out.....

Is there is a hierarchy of preference, and within each level of choice do we reset the rationality clock? i.e. suppose I choose a property investment (my investment preference) as I believe it will maximise my utility over investments X and Y. I am a utility maximising rational econ. However, a layer down, I choose to invest in property B instead of property A, despite property A being a better investment on every financial indicator. I do so, because in this round of choice, property B meets my preference, which is based upon having a new build property, which is closer to home.

I am maximising utility and acting rationally for my new preference, but not in relation to my first preference. In choosing investment B, am I therefor acting rationally or irrationally? Or have I got this all wrong?

*A little disclaimer, this is more me ruminating than providing a rigorously proofed response.

I have never thought of preferences being related that way before, especially through the use of hierarchies.

$$\textbf{Main response}$$

The way I think about the scenario above is through preference weightings, were the values of the goods that can be chosen are weighted according to the good-specific preferences of the agent. This allows the agent to still be a rational econ and maximise their utility, but make sub-optimal financial choices. In a simple scenario similar to your example, there would be two goods, $$X$$ and $$Y$$. $$Y$$ provides greater returns and from what I understand above, the agents utility would take an additive form (to ensure that the goods are substitutes) i.e. $$U_1 = 2Q_Y+Q_X$$ Thus, a utility maximising agent would choose to spend his budget on $$Y$$ as it provides greater returns.

$$\textbf{However}$$, we can incorporate the agents preferences for

a new build property, which is closer to home.

which we can call $$\beta_{nbp}$$. Thus, as $$X$$ has characteristics which match the above, the agents utility would now take the form;

$$\hat {U}_1 = 2Q_Y+\beta_{nbp}\cdot Q_X$$

Thus, the agents utility now incorporates the financial superiority of good $$Y$$, as it outperforms good $$X$$ by a factor of 2, and it incorporates the agents non-financial preferences through $$\beta_{nbp}$$. For a utility maximising agent to choose $$X$$ over $$Y$$, $$\beta_{nbp}$$ must be greater than 2, which implies that the agents non-monetary preferences are more important than his financial preferences. Thus, by adding preference weighting,it is one way to show that a rational utility maximising agent will choose a financially worse product over another product, as there are other non-financial elements which the agent desires more. However, if the agent had been a profit maximiser the choice of $$X$$ over $$Y$$ would not be rational, and in the problem above we would not include $$\beta_{nbp}$$ in the analysis.

$$\textbf{Real life example}$$

A real-life example I suppose which is slightly related, would be choosing between an ultra cheap but crappy mobile(cell) phone and an expensive but good quality phone. On a strictly monetary basis, the ultra cheap one is preferable. However, as soon as you start incorporating quality, the utility-values of the phones change. The change isn't financially, but based on the utility (eg. combined preferences for monetary and non-monetary benefits) derived by whoever is buying the phone, and hence they may choose the better quality phone at the expense of spending more money.

$$\textbf{meta-discussion}$$

On a more meta-level, I think your question has some really interesting points. It appears to be that there is a misinterpretation between utility and profit maximisation. Considering this definition of utility;

utility is the want satisfying power of any commodity or capacity of a commodity to give satisfaction.$$^1$$

It can be seen that utility is not solely reliant on money, but rather is only partially reliant on financial benefits. However, as money is such a large part of our society and can be (relatively)easily measured and compared, it is used a lot to quantify the non-monetary preferences (through monetary trade-offs, which is a really interesting field of research by itself!). Thus, this quantification seems to lead to a bit of confusion between profit maximisation (which is solely focused on money) and utility maximisation (which is focused on utils and want satisfaction), which I wouldn't be surprised is from the way economics is taught and very rarely explicitly mentions this difference. Hence, economics is not necessarily not just solely focused on money, but it does use money to help compare the costs and benefits of tangibles and intangibles. This is probably, a reason why economics is rather practical and often relied upon during policy development, as it provides easily comparable estimates to values which would otherwise be illusive.

$$^1$$ https://en.wikibooks.org/wiki/Principles_of_Economics/Utility

• Many thanks for this comprehensive answer. It is very helpful. – Andrew Nov 5 '18 at 11:53