Getting winners from database per position - Voting system

So I have my data in the table in this format

Candidate Name      Position ID       Total Votes
_____________     _____________     _____________
Name 1                   1                 1
Name 2                   1                 3
Name 3                   2                 1
Name 4                   2                 4
Name 5                   3                 1
Name 6                   3                 5

How can I get the each winners per position. I try many queries but didnt get the right results. Any help would be appreciated.

Solution

Here's a possible solution which could be slightly naïve but I can't seem to be able to think of a better version.

Let us consider a table with the details as follows:

CREATE TABLE VOTING (Name TEXT, position integer, votes integer);
INSERT INTO VOTING VALUES("Name 1", 1, 1);
INSERT INTO VOTING VALUES("Name 2", 1, 3);
INSERT INTO VOTING VALUES("Name 3", 2, 1);
INSERT INTO VOTING VALUES("Name 4", 2, 4);
INSERT INTO VOTING VALUES("Name 5", 3, 1);
INSERT INTO VOTING VALUES("Name 6", 3, 5);

Query is:

SELECT name, 
       A.position, 
       votes 
FROM   voting A, 
       (SELECT position, 
               Max(votes) AS M 
        FROM   voting 
        WHERE  position IN (SELECT DISTINCT( position ) 
                            FROM   voting) 
        GROUP  BY position) B 
WHERE  A.position = B.position 
       AND A.votes = B.m;

My thought process was as follows:

First select all possible distinct position values.
For each distinct position retrieve the max(votes) for that position.
Attach the max(votes) column to the original table where position values match, so that means for each row and position pair there is a max(votes) for that position available.
Filter this new table where position matches and original vote value matches the max(votes) value and you have the table. You can further order these however you want (ASC/DESC)

The result is as follows:

Name    position    votes
------  --------    -----
Name 2  1           3
Name 4  2           4
Name 6  3           5

Here's a link to a running sample: http://sqlfiddle.com/#!9/8d7ce6/54/0