Known as "restored honour", the legal procedure dating back to 1940 does not erase a convict's criminal record, nor is it a pardon.
It is intended to restore a convict's civil rights and help them reintegrate into the community.
But for most Icelanders, the law is obsolete, unjust, and an example of the cronyism that has for too long poisoned politics on the small North Atlantic island of 335,000 people.
Opposition to the law began to emerge after Robert Arni Hreidarsson, a former lawyer who was sentenced to three years in prison in 2007 for having sexually assaulted at least four teenage girls, had his "honour restored" in September 2016.
One of his victims was the daughter of Bergur Thor Ingolfsson, a 48-year-old actor-director who has become a spokesman for the law's opponents.
"I'm really really proud of what we have done, to put a mirror in the face of the system and say 'Look at it, this is crazy'," he told AFP.
Over the past two decades, 86 convicts have applied to have their "honour restored", according to the justice ministry. Thirty-two of them were approved.
"The spirit, the idea of the law was a pretty good thing. But we should put up more fences for people applying for high positions in society," insisted Bergur Thor Ingolfsson.
"Child abusers should not automatically get high positions like police chief, lawyer or member of parliament," he said.
Icelandic prison sentences longer than four months bar convicts from standing for election, taking a seat on the board of a state-owned company, and practising law, among other things.
Atli Gudjon Helgason is an international footballer-turned-lawyer who was sentenced to 16 years in prison for brutally murdering his business associate in 2001. His civil rights were later restored and he was able to recover his licence to practise law.
Another convict who benefitted from "restored honour" told AFP, on condition of anonymity, that he had mixed feelings about the practice.
"For me it was completely necessary because of my education and to have a chance to make a living. I basically had no choice," he said.
"I don't need a document from the government to stipulate that I'm now a good citizen. I broke the law, and I take full responsibility for what I did.
"I was sentenced to prison and finished my sentence. Then I completely turned my life around. This 'restored honour' certificate therefore means nothing to me," he stressed.
Focus on paedophiles
A request for "restored honour", which is granted by the president, must be accompanied by two letters of recommendation signed by upstanding members of the community.
The father of Prime Minister Bjarni Benediktsson, Benedikt Sveinsson, one of Iceland's wealthiest and most influential businessmen, signed such a letter for another paedophile convicted in 2004 of having raped his stepdaughter almost daily for 12 years.
The name of the signatory had been kept from the media and the public (only his son and the justice minister were informed), until a parliamentary commission ordered it be revealed.
Accused of having misled lawmakers and the public, and after a junior coalition member quit the government in protest, the prime minister resigned in September and called a snap election to be held on Saturday.
Icelanders' opposition to the law has focused primarily on child molesters being granted "restored honour", and less so on other types of criminals.
In a bid to address the concerns, parliament voted on September 27 to temporarily repeal a section of the law dealing with those sentenced to more than one year in prison, pending a full review by the future government.
But Arnar Thor Jonsson, a lawyer and former Reykjavik judge, lamented that some convicts are now no longer able to benefit from rehabilitation.
"The debate has been focused too narrowly on paedophiles," he said.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
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