Why are niceness values inversely related to process priority?

@Ewald's answer is correct, as is confirmed by Jerry Peek et al. in Unix Power Tools (O'Reilly, 2007, p. 507):

This is why the nice number is usually called niceness: a job with a high niceness is very kind to the users of your system (i.e., it runs at low priority), while a job with little niceness hogs the CPU. The term "niceness" is awkward, like the priority system itself. Unfortunately, it's the only term that is both accurate (nice numbers are used to compute the priorities but are not the priorities themselves) and avoids horrible circumlocutions ("increasing the priority means lowering the priority...").

Nice has had this meaning since at least V6 Unix, but the V6 manual never explains this explicitly. The range of allowed values was -220 through +20, with negative numbers reserved for the superuser. The range was changed to -20 through +20 in V7.

Hysterical reasons - I mean historical... I'm pretty sure it started with numbers going up from 0 .. 20, and the lowest available was taken first. Then someone came to the conclusion that "Hmm, what if we need to make some MORE important" - well we have to go negative.

You want priority to be a sortable value, so if you start with "default is zero", you have to either make higher priority a higher number (but "priority 1" in daily speak is higher then "priority 2" - when your boss says "Make this your number 1 priority", it does mean it's important, right?). Being a computer, clearly priority 0 is higher than priority 1, and priority -1 is higher than priority 0.

In the end, it's an arbitrary choice. Maybe Ken Thomson, Dennis Ritchie or one of those guys will be able to say for sure why they choose just that sequence, and not 0..255, for example.

First of all the answer is a little bit long but it is only for clarification.

As in the linux kernel every conventional process may have the priorities which are called static priority are from 100(highest) to 139(lowest). so there are basically 40 priorities which could be assigned to the process.

so when any process is created it gets the priority of it's parent but if the user wants to change it's priority then it could be done with the help of nice(nice_value) system call.

& the reason for your question is that every process wants base time quantum which is used as how much time the process will get the CPU for its execution in milliseconds and this is calculated as

time={     if static_priority<120       (140-static_priority)*20      if static_priority>=120       (140-static_priority)*5

so The sys_nice( )service routine handles the nice( )system call. Although the nice_value may have any value, absolute values larger than 40 are trimmed down to 40. Traditionally, negative values correspond to requests for priority increments and require superuser privileges, while positive ones correspond to requests for priority decreases. In the case of a negative nice_value, the function invokes the capable( ) function to verify whether the process has a CAP_SYS_NICE capability. Moreover, the function invokes the security_task_setnice( )security hook. so in the end the nice_value is used to calculate the static priority & then this static priority is used for calculation of base time quantum.

so it's clear that -ve values are used for increment the priority so needs super user access & +ve values are used for decrease the priority so no need of super user access.