The output has to be burned  otherwise there is no cost of expressing
any number of alternate opinions the same time. 

Tamas Blummer
Bits of Proof

On Dec 15, 2014, at 3:55 PM, Isidor Zeuner <cryptocurrencies@quidecco.de> wrote:
> For every participant who could try to decide about the adequateness
> of the cost, no direct effect comes from the difference between Proof
> of Burn, and approaches which keep the Bitcoins inside the set of
> outputs that can still participate. So, any notion which
> differentiates with respect to this must make some assumption about
> what defines the interest of the Bitcoin nodes as a community.
> 
> Best regards,
> 
> Isidor
>