Why do we want what we don't have? There are many different answers stemming from diverse theoretical approaches. I will list a couple, drawing heavily on a older review by Lynn (1992) who has collected different ideas about why desirability can sometimes be increased when something is unavailable to us.
We perceive things that few people have as important resources that signal social status. This can be seen in people's tendency for conspicuous consumption (Veblen, 1899), in other words the tendency to buy positional goods, which promise being superior to others (e.g. Solnick & Hemenway, 1998)
Researchers such as Snyder and Fromkin (1977) posit that people can perceive similarity to others as a threatening. Therefore, scarce and unavailable things are desirable because they promise to fulfill a need for uniqueness.
Unavailable resources often imply that having them means to have power over others (Emerson, 1962)
Social comparisons can give rise to specific emotions that motivate us to seek things that are unavailable. People deliberately engage in downward comparisons (Wills, 1981) to enhance their self-esteem. Having something that not everybody has may thus give rise to pride. Upward comparisons with others (who have something we want) may cause envy, which can increase desire (Crusius & Mussweiler, 2012, Van de Ven et al. 2011)
Scarcity has been portrayed as a heuristic cue that signals desirability (Cialdini, 1993), for example, because rare things are perceived to have a higher quality (Ditto & Jemmott, 1989)
Sometimes, we don't have things because we are denied to have them. Such threats to our freedom cause reactance which increases our desire to have what we can't have (e.g., Brehm, Stires, Sensenig, & Shaban, 1966)
Trying to attain something which is difficult to get increases arousal which fuels desirability (Brehm et al, 1983)
It stands to reason, however, that we are often quite good in rationalizing why we don't want the things that we don't have (e.g., Kay, Jimenez, & Jost, 2002).
Brehm, J. W., Stires, L. K., Sensenig, J., & Shaban, J. (1966). The attractiveness of an eliminated choice alternative. Journal of Experimental Social Psychology, 2, 301–313. doi:10.1016/0022-1031(66)90086-2
Brehm, J. W., Wright, R. A., Solomon, S., Silka, L., & Greenberg, J. (1983). Perceived difficulty, energization, and the magnitude of goal valence. Journal of Experimental Social Psychology, 19, 21–48. doi:10.1016/0022-1031(83)90003-3
Brock, T. C. (1968). Implications of commodity theory for value change. In A. G. Greenwald, T. C. Brock, & T. M. Ostrom (Eds.), Psychological foundations of attitudes (pp. 243–275). New York: Academic Press.
Cialdini, R. B. (1993). Influence: Science and practice (3rd ed.). New York: HarperCollins.
Crusius, J., & Mussweiler, T. (2012). When people want what others have: The impulsive side of envious desire. Emotion, 12, 142–153. doi:10.1037/a0023523
Ditto, P. H., & Jemmott, J. B. (1989). From rarity to evaluative extremity: Effects of prevalence information on evaluations of positive and negative characteristics. Journal of Personality and Social Psychology, 57, 16–26. doi:10.1037/0022-35184.108.40.206
Emerson, R. M. (1962). Power-dependence relations. American Sociological Review, 27, 31-41.
Kay, A. C., Jimenez, M. C., & Jost, J. T. (2002). Sour grapes, sweet lemons, and the anticipatory rationalization of the status quo. Personality and Social Psychology Bulletin, 28, 1300–1312. doi:10.1177/01461672022812014
Lynn, M. (1992). The psychology of unavailability: Explaining scarcity and cost effects on value. Basic & Applied Social Psychology, 13, 3–7. doi:Article
Snyder R., C., & Fromkin, H. L. (1977). Abnormality as a positive characteristic: The development and validation of a scale measuring need for uniqueness. Journal of Abnormal Psychology, 86, 518–527. doi:10.1037/0021-843X.86.5.518
Solnick, S. J., & Hemenway, D. (1998). Is more always better? A survey on positional concerns. Journal of Economic Behavior & Organization, 37, 373–383. doi:10.1016/S0167-2681(98)00089-4
Van de Ven, N., Zeelenberg, M., & Pieters, R. (2011). The envy premium in product evaluation. The Journal of Consumer Research, 37, 984–998. doi:10.1086/657239
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Wills, T. A. (1981). Downward comparison principles in social psychology. Psychological Bulletin, 90, 245–271. doi:10.1037/0033-2909.90.2.245