In the UK, a country of more than 66 million people , the voices or Northern Irish voters regularly get overlooked as they represent less than 3%  of the country.
The impotence of Northern Irish voters in British democracy was on display in the Brexit referendum of 2016, when a majority of voters in Northern Ireland chose to remain in the European Union , but found their vote overwhelmed by the much larger population of Great Britain. Similarly, only 12 of the 650 seats in the House of Commons represent Northern Ireland, again making it very difficult for Northern Irish political views to have any impact on the governance of the territory. Northern Ireland only exerts real influence in the House of Commons during a hung parliament when a major party must rely on a Northern Irish party to form a coalition to govern, and even then only one party can exert influence at a time. A united Ireland, however, would be home to less than 7 million people, of which more than a quarter would be from what is now Northern Ireland, guaranteeing the territory a much more substantial political influence. Even if the Northern Irish vote remains divided, as it likely will, each bloc would make up more than a tenth of Ireland's voters. In addition, Ireland's single transferable vote electoral system could allow for minority voices within constituencies to be represented in the Dail, whereas in Westminster, MPs may only gain support from one side of the community due to first-past-the-post voting.
The United Kingdom has mostly devolved issues that affect Northern Ireland to the Northern Irish government in Stormont. Northern Irish voters decide who sits in Stormont, giving Northern Irish residents the autonomy to determine how they are governed. While disagreements have led to its dissolution, it may well return soon and when it does, Northern Irish voters will have a greater voice and more autonomy than they would have in a United Ireland. Even if Ireland does introduce provincial governments, the value of a Northern Irish vote would likely decline slightly as the other three counties of Ulster - Cavan, Monaghan and Donegal - are added to the Assembly. The United Kingdom is also set to become more democratic and allow voters a greater voice as it leaves the European Union. Meanwhile, the Republic of Ireland will remain under the eye of Brussels, which passes laws with virtually no input from the Irish voter. In addition, the United Kingdom represents many diverse viewpoints and backgrounds: there is not a single, consistent "British" vote that is stifling Northern Ireland. Even within England, differences between voters are strong. Ireland, on the other hand, is so dominated by the size and economic power of Dublin that voters from the capital could easily form a single bloc to quash Northern Irish objectives.
[P1]: Northern Ireland would make up a larger part of Ireland's population than the UK's [P2]: In both countries' systems, smaller groups exert less political power [P3]: Therefore, Northern Irish voters would exert more power in a united Ireland
Rejecting the premises
[Rejecting P2] In a larger country like the UK, local issues can be devolved to ensure smaller groups can still wield significant political power