Re: Easy solution. Win your patent case, collect. Lose, pay 10 times + legal fees.
While this seems like a great idea at first, there are problems with making the loser pay like that.
Primarily it discourages people or companies with valid patents from suing unless they think they have a extremely good chance of winning (>90%).
So, I expect the response to this, is that the law should only apply to patent trolls. Now you just have to effectively define what constitutes a patent troll. Non-practicing entities are one of the more popular descriptions, but that would include any inventor who doesn't have the means to produce his invention, but doesn't want to sell it outright to a company. Likewise, non-practicing entity also excludes those large corporations that simply collect tons of patents as a way of beating their competition into submission.
While not as simple a rule, it would work better to allow the judge to assess penalties--perhaps up to your 10x--in the case of bad faith litigation, where the litigant clearly is a troll and is simply trawling for suckers. Some trolls may luck out, but far fewer honest patent holders will get caught up. And in some ways, invalidating the patents does exactly this, if only on a small scale.