The brothers live on the island of Brecqhou, next to Sark
The Supreme Court has unanimously dismissed an appeal case by the Barclay brothers who wanted to force a change to constitutional reforms on Sark.
Sir David and Frederick Barclay argued reforms did not go far enough because two of the members of the island's government were not elected.
The ruling said the offices of seigneur and seneschal were not contrary to the European Convention on Human Rights.
The 28 elected conseillers replaced 450 years of feudal rule in the island.
The Barclays, proprietors of the Daily Telegraph, live on the nearby island of Brecqhou and own land on Sark, which has a population of about 600.
They argued Sark's new constitution and the dual role of the seneschal did not meet the modern standards set by European and UK human rights laws with regard to elections.
When their case reached the Court of Appeal, judges refused to declare the Reform (Sark) Law 2008 "incompatible" with the ECHR on the grounds that it did not meet the human rights requirements of free and fair elections.
The pair decided to take their battle to the House of Lords, but their challenge was unanimously dismissed by five justices.
The island's first election to choose a democratic government for nearly 450 years took place on 10 December 2008.
A day later, the twins announced they were withdrawing their business interests in Sark.
The move resulted in the closure of a number of shops and hotels and the loss of up to 100 jobs.
The news brought tens of thousands of pounds in donations from neighbouring islands to support those out of work.
The decision was reserved on 24 December when it was announced the majority of businesses would re-open.
Vote for democracy
Sark has been governed by a mix of landowners and elected people's deputies since the 1600s, with landowners automatically getting a seat.
This system was replaced after islanders voted for democracy in a referendum, before the reform was approved by the Privy Council in April 2008.
Sark's new Chief Pleas, the island's government, was installed on 9 January 2009 with 28 elected members or conseillers joining the seigneur and seneschal in the chamber.
The seigneur is the head of the Chief Pleas and retains feudal rights and the seneschal is president of the Chief Pleas and head of the judiciary.
Neither have the right to vote on Chief Pleas, although the seigneur is able to speak.