I made my own query using SEDE.

It looks at votes cast per person (no matter when they were cast). If you know how long the site has been around, you could calculate average votes per day.

It's an easy and fast query actually:

select count(id), avg(upvotes), avg(downvotes), sum(upvotes), sum(downvotes) 
from users

I use the above query to get the data for all users. For "new" users, I add where reputation<150 and for "avid" users, I add where reputation>=150.

Results:

------------- + Count + Avg Up + Avg Down +   Up   + Down 
-- All   users| 94897 |    4   |    0     | 395650 | 35461
--"Avid" users|  6284 |   51   |    5     | 322880 | 32620
--"New"  users| 88613 |    0   |    0     |  72770 |  2841 

The average is really brought down by the new users, who obviously don't spend as much time on the site (and therefore vote less). There's not really a way to force them to vote (many of them will likely never visit again). Some of them might not yet have the privilege (although this is rare), or may have no interest in doing so.

Personally, I think this community is very open with votes, especially compared with sites like Stack Overflow (where I have posted hundreds of answers that sit at 0 score).

I also ran the query against every site. I'm not going to make a table for that, since it's a lot of data. My query (which uses my first query):

declare  db_c cursor for select [name] 
       from sys.databases 
       where database_id > 5 -- skip master, temp, model, msdb, Data.SE

declare @db_c_name sysname   -- holds name of db after fetch
declare @sql nvarchar(max) -- holds build up sql string

-- result table
create table #all_users (
    name nvarchar(40)
    , users int
    , avgUp int
    , avgDn int
    , totalUp int
    , totalDown int
);

open db_c
fetch next from db_c into @db_c_name
while(@@FETCH_STATUS = 0)
begin
    set @sql = N'use '+ QUOTENAME(@db_c_name) +';
    insert into #all_users 
    select
    '''+ 
       QUOTENAME(@db_c_name) +
    '''
    ,count(id), avg(upvotes), avg(downvotes), sum(upvotes), sum(downvotes) 
    from users
    ';
    exec (@sql)
   fetch next from db_c into @db_c_name
end;
close db_c;
deallocate db_c;

select * from #all_users 

(The same modifications need to be done to check for avid and new users.)