In contrast to republic/representative government, direct democracy aims to give every individual citizen equal chance to influence outcomes. Whereas progressives tend to see moving in this direction as an unmitigated good, conservatives see the aspiration with wariness. These positions reflect different evaluations of the ‘wisdom of crowds’ - trustworthy vs. dangerous.
Conservatives have historically seen dialogue and deliberation as dangerously trying to supplant representative democracy with direct democracy.
Arguably one of the most prominent examples of “direct democracy” are California’s initiatives and referendums, through which voters vote directly on laws rather than allowing them to work through the standard representative process. Both progressives and conservatives have at different times been frustrated with this process. For instance, Proposition 13 famously limited property taxes in California, a limitation which many progressives find frustrating.