Selecting, ranking and applying a point score based on rank
Sample data:

CREATE TABLE v
    (`vote` varchar(8), `game` int, `year` int)
;

INSERT INTO v
    (`vote`, `game`, `year`)
VALUES
    ('player 1', 2, 2015),
    ('player 1', 2, 2015),
    ('player 2', 2, 2015),
    ('player 2', 2, 2015),
    ('player 2', 2, 2015),
    ('player 3', 2, 2015),
    ('player 1', 2, 2015),
    ('player 3', 2, 2015),
    ('player 4', 2, 2015)
;


Query:

SELECT 
vote,
no_votes,
rank,
3 - rank + (1 / CASE rank WHEN 1 THEN @rc1 WHEN 2 THEN @rc2 WHEN 3 THEN @rc3 END) AS points
FROM (

    SELECT 
    sq.*
    , @rank := if(@prevNoVotes = no_votes, @rank, @rank + 1) AS rank
    , @rc1 := if(@rank = 1, @rc1 + 1, @rc1)
    , @rc2 := if(@rank = 2, @rc2 + 1, @rc2)
    , @rc3 := if(@rank = 3, @rc3 + 1, @rc3)
    , @prevNoVotes := no_votes
    FROM
    (

        SELECT 
        vote, 
        COUNT(*) AS no_votes
        FROM v
        GROUP BY vote

    ) sq
    , (SELECT @rank := 0, @prevNoVotes := null, @rc1 := 0, @rc2 := 0, @rc3 := 0) var_init_subquery
    ORDER BY no_votes DESC

) q


Result:

|     VOTE | NO_VOTES | RANK | POINTS |
|----------|----------|------|--------|
| player 1 |        3 |    1 |    2.5 |
| player 2 |        3 |    1 |    2.5 |
| player 3 |        2 |    2 |      2 |
| player 4 |        1 |    3 |      1 |



see it working live in an sqlfiddle


Explanation:

This

        SELECT 
        vote, 
        COUNT(*) AS no_votes
        FROM v
        GROUP BY vote


is simple enough, I hope :)

This

, (SELECT @rank := 0, @prevNoVotes := null, @rc1 := 0, @rc2 := 0, @rc3 := 0) var_init_subquery


is just a subquery to initialize some variables. 

Here

    , @rank := if(@prevNoVotes = no_votes, @rank, @rank + 1) AS rank
    , @rc1 := if(@rank = 1, @rc1 + 1, @rc1)
    , @rc2 := if(@rank = 2, @rc2 + 1, @rc2)
    , @rc3 := if(@rank = 3, @rc3 + 1, @rc3)
    , @prevNoVotes := no_votes


in the first row @prevNoVotes holds the value of the previous row (or the value from the initialization subquery). @rc1, @rc2 and @rc3 are just rank counters. They count for each rank, how many people are on the same rank.
In the last row, the value of the current row is assigned to the variable. When the next row is processed, the variable will hold the value of the previous row in the first line of this part of the code.

And finally in the most outer part of the query we calculate the points distribution.

Feel free to ask any questions :)

UPDATE:

Added this table:

CREATE TABLE points
    (`r` int, `p` int)
;

INSERT INTO points
    (`r`, `p`)
VALUES
    (1, 3),
    (2, 2),
    (3, 1)
;


Added more logic :)

SELECT 
vote,
no_votes,
rank,
@rc := @rc + 1 AS rowcounter,
((SELECT p FROM points WHERE r = IF(rank = @prevRank, rank, @rc)) - 1) + (1 / CASE rank WHEN 1 THEN @rc1 WHEN 2 THEN @rc2 WHEN 3 THEN @rc3 END) AS points,
@prevRank := rank
FROM (
    SELECT 
    sq.*
    , @rank := if(@prevNoVotes = no_votes, @rank, @rank + 1) AS rank
    , @rc1 := if(@rank = 1, @rc1 + 1, @rc1)
    , @rc2 := if(@rank = 2, @rc2 + 1, @rc2)
    , @rc3 := if(@rank = 3, @rc3 + 1, @rc3)
    , @prevNoVotes := no_votes
    FROM
    (

        SELECT 
        vote, 
        COUNT(*) AS no_votes
        FROM v
        GROUP BY vote

    ) sq
    , (SELECT @rank := 0, @prevNoVotes := null, @rc1 := 0, @rc2 := 0, @rc3 := 0) var_init_subquery
    ORDER BY no_votes DESC
)q
, (SELECT @rc := 0, @prevRank := 1) row_counter_init
ORDER BY rank



see it working live in this sqlfiddle