My best suggestion yet. In fact, with hindsight, all my other suggestions sucked.
At BlizzCon 2011, Wyatt Cheng said that in Hardcore PvP, players will not die permanently like they do in the regular game. This makes sense to me, as a hardcore player will be careful in PvE, usually surviving very many hours without dieing, while in PvP, careful is not an option, and you would have a high chance of losing those very many hours of character development in under a minute every single time you play PvP. Yes, it would be exhilarating, just like almost dieing or dieing in Hardcore PvE, but the rate at which people die in PvP is far too high to justify that feeling - Diablo 3 arena PvP will be built around dieing and re-spawning very quickly, since the winner of the game will reportedly be the team that get the most kills / least deaths in 10 minutes.
Some have suggested having a deadly duel option, in which the loser would die permanently. I have an alternate idea.
Suggestion: High-Stake Duelling (aka racing for pink slips)
If you die in a high-stake duel, you will not die permanently, but you WILL lose all of your equipped items, as all of your eqiupped items would be given to the victor.
This option could not be available in softcore, as it would most definitely encourage real money gambling (in these cases, buying expensive items with real money with the objective of turning a profit by making more real money).
Auto-Listing of items won from High-Stake duels
Upon winning, the victor would be prompted with an option to list each of the items won on the HC GAH. Thus, the victor would be able to look through the items won and keep those he wants to keep, then select the option to sell the rest of them on the HC GAH. By selecting this option, all of the items the victor won but did not choose to keep will instantly be listed on the HC GAH and have their listing fees waived. If the victor chooses to keep an item won, then later sell it on the HC GAH, the listing fee will not be waived, since they did not choose to use this auto-list feature that is available only immediately after winning the high-stake duel.
Also, when the victor lists any of the items won using this auto-list feature, the loser will be prompted with a link to the listings of these items on the HC GAH - the loser can buy back the items the victor won and chose to auto-list, but will have to be willing to beat out other bids on the GAH, and to have enough gold to do so!
This option for Hardcore players to "race for pinks" would be intense. You wouldn't want to risk losing your best and most expensive items, but if you duel without them, you will more probably lose! Those who lose more than they win will be in an uphill battle; when they lose, they will lose all their equipped items, which are probably their best items, and will have to start over looking for good items, or spend a lot of money buying their items back - if they have that much money! Those who win more than they lose will be on top of the world; even if they lose a duel, they will probably have already won a couple of other people's items and sold most of them, so that they have enough money to buy their item set back or buy a new item set.
"...the losers WILL hand over them keys. Otherwise, you'll be eating breakfast through straws from now on." ~Ludacris