Machine politics in Chicago has been described as a successful example of exchange theory in which political party members received benefits in return for loyalty to the party. In 1988, Erie rejected the rainbow theory of machine politics, arguing that the Irish received the lion's share of political benefits while other white-ethnic groups, such as Poles, were given limited and often symbolic rewards. These authors show that Chicago's Poles were not fully incorporated into the rainbow of groups that benefited from and supported the machine. This led to a pattern of independence in voting and lends considerable support to Erie's supply-side model of machine politics.