A single ballot box served Velioldugu at the 2023 parliamentary election, with 51 registered voters; that places it 109th among the 123 localities of Sorgun.
The village parts ways with the district as a whole. At the 2023 parliamentary election it went to İYİ Parti with 34 votes, while across Sorgun the leading party was AK Parti, with İYİ Parti here running 70.3 points above its district average. In the presidential runoff, 41 of 45 valid votes went to Kemal Kılıçdaroğlu — 74.1 points above the district average. At the 2017 referendum 26 of 35 valid votes were 'no' — 56.2 points above the district average.
At the 2024 local election the village went to CHP with 50 votes, while Sorgun as a whole was won by MHP. Turnout at the 2024 local election was 94.5%, 12.9 points above the district average. The tightest race came at the 2014 local election: MHP took 20 votes to CHP's 17 — a margin of just 3 votes. First place has changed hands 5 times here since 2009.