Preferences of an individual can be understood as a ranking of alternatives depending on the level of happiness and utility that can be brought to the individual. In order for ranking of preferences, the individual needs to be rational. i.e He can't say i don't know, although he can say for instance, i have the same preference for Apples and Oranges. As such, economists need 2 main conditions:
Completeness and Transitivity
Completeness:
A ranking can be complete only if all the possible combinations of bundles of good can be ranked. For instance, assuming for an individual, there exists a basket of fruit of 3 apples (A) and 3 oranges (O), totalling 6 fruits. This is the bundle of goods that the individual possesses. With his bundle of goods, he will be able to rank all the different combinations of apples and oranges. For instance, he can have a complete ranking preference by choosing the combination of 0A and 3O or 1A and 3O or 2A and 2O etc and the list goes on. As long as all the possible combinations of bundles of goods are accounted for, his ranking is complete.
Transitivity:
This concept requires rational behavior. For instance, you have 3 options of goods: Sandwiches, Hotdogs and Burgers and you are asked by your mum to choose the preferences for what to have for lunch. After a moment, you decided that you prefer sandwiches to Hotdog and hotdogs to burgers. From here, if you are a rational person, you will be implying that you prefer Sandwiches to Burgers since:
Sandwich > Hotdogs > Burgers
=> Sandwich > Burgers
The > here refers to preferences and not the usual more or less function. This concept can be known as transitivity. I.e. your preferences are transitive. However, if your decisions are not rational, you may choose burgers over sandwich which does not really make sense.
=> Burger > Sandwich
This is not a rational decsions as based on your ranking above in the decision matrix since you have ranked sandwiches as the top food that you want to consume and burgers as the last.
Once ranking of preferences can be complete and transitive : Your preferences will be rational.
Utilities can be understood as numbers that will help determine the level of happiness of the individual to aid in his ranking of preferences. In the process of preferences ranking, an individual will rank the bundle of good (X,Y) that gives the highest utility above the rest. However, it is important to note that a utility function that generates a number that has twice the amt of another bundle of good does not mean that the particular bundle is twice preferred or twice as good. The numbers generated from these functions serve as a guide for placement of ranking. Allow me to elaborate with an example:
Using a very basic utility function : U(X,Y) = X+Y
If X = 1 and Y = 1 => This will give a utility of 2
If X= 2 and Y = 2 => This will give a utility of 4
Taking that utility functions takes only positive transformation, certainly a utility of 4 gives higher satisfaction or happiness as compared to a utility of 2 (You will always prefer more to less unless you have reached a satiation point, which will be elaborated in other posts). However, this does not mean that 2+2 is twice as good as 1+1.
For example: if X is apple and Y is orange, have a total of 4 fruits in your basket does not means that you are twice as satisfied or twice as happy. Why? We of think of it simply as happiness and satisfaction are intangible materials that can't be quantified. However, we can quantify that having twice the amount of apple and orange will make you more happy as you have more fruits to eat, assuming that it has not reached your satiation point.
By the way, the utility function above refers to one of perfect subsitutes which will be elaborated in future posts. More examples will be posted for different utility functions in future posts
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