I’ve never seen the series in question, but in the UK at least, the outcome of a tied parliamentary constituency vote in a General Election, or a local election for councillors can be resolved by a coin toss or other fair test.
This has happened as recently as 2017 in a local election, where two candidates drew straws.
Obviously, this is after several recounts to ensure the numbers are accurate.
In terms of how far up this goes, there is no direct voting for any higher office than your local Member of Parliament (MP) as the Prime Minister is appointed by the Queen and is the person who leads the majority of MPs in Parliament. Whilst a tie has never happened in a UK General Election parliamentary vote, it is a valid process.
Other countries may vary.