My thesis mainly discusses the extent of redistribution in a democratic society. In poor and unequal societies, the income distribution is typically skewed to the right. Standard electoral models of politics predict that the above case would lead to a large extent of redistribution. Empirical studies, however, show weak support for this theory. Some researchers even find the opposite relationship between income inequality and redistribution.In my thesis, I will review some theoretical arguments that have been developed to explain the apparent limitation of the electoral theory of redistribution. Then I will introduce a new model in which citizens may have different preferences for publicly provided goods. Citizens will then have different willingness to pay for it, which in turn affects the equilibrium redistribution policy. For instance, some rich people may less prefer publicly provided health service (may be due to low quality of the same), and so, they turn to buy it in the private market if it is available there. So those people may benefit less from the policy that adopts to spend a lot on the social health system, and this would result in low willingness to pay tax for the publicly provided good. We parameterize citizens’ intention to consume the publicly provided goods into the model, which provides us with a new term for the pivotal voter. Finally,I study how individuals make the choice between these two markets. How many people in proportion of the whole population will choose the good supplied by the private manufacturer, how the private manufacturer and the government determine the quality of the good they provided respectively, how the price of the good in the private market is formulated, and what is the equilibrium tax rate in this circumstance.