Runoff
Problem to Solve
You already know about plurality elections, which follow a very simple algorithm for determining the winner of an election: every voter gets one vote, and the candidate with the most votes wins.
But the plurality vote does have some disadvantages. What happens, for instance, in an election with three candidates, and the ballots below are cast?
A plurality vote would here declare a tie between Alice and Bob, since each has two votes. But is that the right outcome?
There’s another kind of voting system known as a ranked-choice voting system. In a ranked-choice system, voters can vote for more than one candidate. Instead of just voting for their top choice, they can rank the candidates in order of preference. The resulting ballots might therefore look like the below.
Here, each voter, in addition to specifying their first preference candidate, has also indicated their second and third choices. And now, what was previously a tied election could now have a winner. The race was originally tied between Alice and Bob, so Charlie was out of the running. But the voter who chose Charlie preferred Alice over Bob, so Alice could here be declared the winner.
Ranked choice voting can also solve yet another potential drawback of plurality voting. Take a look at the following ballots.
Who should win this election? In a plurality vote where each voter chooses their first preference only, Charlie wins this election with four votes compared to only three for Bob and two for Alice. But a majority of the voters (5 out of the 9) would be happier with either Alice or Bob instead of Charlie. By considering ranked preferences, a voting system may be able to choose a winner that better reflects the preferences of the voters.
One such ranked choice voting system is the instant runoff system. In an instant runoff election, voters can rank as many candidates as they wish. If any candidate has a majority (more than 50%) of the first preference votes, that candidate is declared the winner of the election.
If no candidate has more than 50% of the vote, then an “instant runoff” occurrs. The candidate who received the fewest number of votes is eliminated from the election, and anyone who originally chose that candidate as their first preference now has their second preference considered. Why do it this way? Effectively, this simulates what would have happened if the least popular candidate had not been in the election to begin with.
The process repeats: if no candidate has a majority of the votes, the last place candidate is eliminated, and anyone who voted for them will instead vote for their next preference (who hasn’t themselves already been eliminated). Once a candidate has a majority, that candidate is declared the winner.
Sounds a bit more complicated than a plurality vote, doesn’t it? But it arguably has the benefit of being an election system where the winner of the election more accurately represents the preferences of the voters. In a file called runoff.c
in a folder called runoff
, create a program to simulate a runoff election.
Demo
Distribution Code
Download the distribution code
Log into cs50.dev, click on your terminal window, and execute cd
by itself. You should find that your terminal window’s prompt resembles the below:
$
Next execute
wget https://cdn.cs50.net/2024/fall/psets/3/runoff.zip
in order to download a ZIP called runoff.zip
into your codespace.
Then execute
unzip runoff.zip
to create a folder called runoff
. You no longer need the ZIP file, so you can execute
rm runoff.zip
and respond with “y” followed by Enter at the prompt to remove the ZIP file you downloaded.
Now type
cd runoff
followed by Enter to move yourself into (i.e., open) that directory. Your prompt should now resemble the below.
runoff/ $
If all was successful, you should execute
ls
and see a file named runoff.c
. Executing code runoff.c
should open the file where you will type your code for this problem set. If not, retrace your steps and see if you can determine where you went wrong!
Hints
Understand the code in runoff.c
Whenever you’ll extend the functionality of existing code, it’s best to be sure you first understand it in its present state.
Look at the top of runoff.c
first. Two constants are defined: MAX_CANDIDATES
for the maximum number of candidates in the election, and MAX_VOTERS
for the maximum number of voters in the election.
// Max voters and candidates
#define MAX_VOTERS 100
#define MAX_CANDIDATES 9
Notice that MAX_CANDIDATES
is used to size an array, candidates
.
// Array of candidates
candidate candidates[MAX_CANDIDATES];
candidates
is an array of candidate
s. In runoff.c
a candidate
is a struct
. Every candidate
has a string
field for their name
, an int
representing the number of votes
they currently have, and a bool
value called eliminated
that indicates whether the candidate has been eliminated from the election. The array candidates
will keep track of all of the candidates in the election.
// Candidates have name, vote count, eliminated status
typedef struct
{
string name;
int votes;
bool eliminated;
}
candidate;
Now you can better understand preferences
, the two-dimensional array. The array preferences[i]
will represent all of the preferences for voter number i
. The integer, preferences[i][j]
, will store the index of the candidate, from the candidates
array, who is the j
th preference for voter i
.
// preferences[i][j] is jth preference for voter i
int preferences[MAX_VOTERS][MAX_CANDIDATES];
The program also has two global variables: voter_count
and candidate_count
.
// Numbers of voters and candidates
int voter_count;
int candidate_count;
Now onto main
. Notice that after determining the number of candidates and the number of voters, the main voting loop begins, giving every voter a chance to vote. As the voter enters their preferences, the vote
function is called to keep track of all of the preferences. If at any point, the ballot is deemed to be invalid, the program exits.
Once all of the votes are in, another loop begins: this one’s going to keep looping through the runoff process of checking for a winner and eliminating the last place candidate until there is a winner.
The first call here is to a function called tabulate
, which should look at all of the voters’ preferences and compute the current vote totals, by looking at each voter’s top choice candidate who hasn’t yet been eliminated. Next, the print_winner
function should print out the winner if there is one; if there is, the program is over. But otherwise, the program needs to determine the fewest number of votes anyone still in the election received (via a call to find_min
). If it turns out that everyone in the election is tied with the same number of votes (as determined by the is_tie
function), the election is declared a tie; otherwise, the last-place candidate (or candidates) is eliminated from the election via a call to the eliminate
function.
If you look a bit further down in the file, you’ll see that the rest of the functions—vote
, tabulate
, print_winner
, find_min
, is_tie
, and eliminate
—are all left to up to you to complete! You should only modify these functions in runoff.c, though you may #include additional header files atop runoff.c if you’d like.
Complete the vote
function
Complete the vote
function.
- The function takes three arguments:
voter
,rank
, andname
. - If
name
is a match for the name of a valid candidate, then you should update the global preferences array to indicate that the votervoter
has that candidate as theirrank
preference. Keep in mind0
is the first preference,1
is the second preference, etc. You may assume that no two candidates will have the same name. - If the preference is successfully recorded, the function should return
true
. The function should returnfalse
otherwise. Consider, for instance, whenname
is not the name of one of the candidates.
As you write your code, consider these hints:
- Recall that
candidate_count
stores the number of candidates in the election. - Recall that you can use
strcmp
to compare two strings. - Recall that
preferences[i][j]
stores the index of the candidate who is thej
th ranked preference for thei
th voter.
Complete the tabulate
function
Complete the tabulate
function.
- The function should update the number of
votes
each candidate has at this stage in the runoff. - Recall that at each stage in the runoff, every voter effectively votes for their top-preferred candidate who has not already been eliminated.
As you write your code, consider these hints:
- Recall that
voter_count
stores the number of voters in the election and that, for each voter in our election, we want to count one ballot. - Recall that for a voter
i
, their top choice candidate is represented bypreferences[i][0]
, their second choice candidate bypreferences[i][1]
, etc. - Recall that the
candidate
struct
has a field calledeliminated
, which will betrue
if the candidate has been eliminated from the election. - Recall that the
candidate
struct
has a field calledvotes
, which you’ll likely want to update for each voter’s preferred candidate. - Recall that once you’ve cast a vote for a voter’s first non-eliminated candidate, you’ll want to stop there, not continue down their ballot. You can break out of a loop early using
break
inside of a conditional.
Complete the print_winner
function
Complete the print_winner
function.
- If any candidate has more than half of the vote, their name should be printed and the function should return
true
. - If nobody has won the election yet, the function should return
false
.
As you write your code, consider this hint:
- Recall that
voter_count
stores the number of voters in the election. Given that, how would you express the number of votes needed to win the election?
Complete the find_min
function
Complete the find_min
function.
- The function should return the minimum vote total for any candidate who is still in the election.
As you write your code, consider this hint:
- You’ll likely want to loop through the candidates to find the one who is both still in the election and has the fewest number of votes. What information should you keep track of as you loop through the candidates?
Complete the is_tie
function
Complete the is_tie
function.
- The function takes an argument
min
, which will be the minimum number of votes that anyone in the election currently has. - The function should return
true
if every candidate remaining in the election has the same number of votes, and should returnfalse
otherwise.
As you write your code, consider this hint:
- Recall that a tie happens if every candidate still in the election has the same number of votes. Note, too, that the
is_tie
function takes an argumentmin
, which is the smallest number of votes any candidate currently has. How might you usemin
to determine if the election is a tie (or, conversely, not a tie)?
Complete the eliminate
function
Complete the eliminate
function.
- The function takes an argument
min
, which will be the minimum number of votes that anyone in the election currently has. - The function should eliminate the candidate (or candidates) who have
min
number of votes.
Walkthrough
How to Test
Be sure to test your code to make sure it handles…
- An election with any number of candidate (up to the
MAX
of9
) - Voting for a candidate by name
- Invalid votes for candidates who are not on the ballot
- Printing the winner of the election if there is only one
- Not eliminating anyone in the case of a tie between all remaining candidates
Correctness
check50 cs50/problems/2024/fall/runoff
Style
style50 runoff.c
How to Submit
Per Step 4 below, after you submit, be sure to check your autograder results. If you see SUBMISSION ERROR: missing files (0.0/1.0)
, it means your file was not named exactly as prescribed (or you uploaded it to the wrong problem).
Correctness in submissions entails everything from reading the specification, writing code that is compliant with it, and submitting files with the correct name. If you see this error, you should resubmit right away, making sure your submission is fully compliant with the specification. The staff will not adjust your filenames for you after the fact!
- Download your
runoff.c
file by control-clicking or right-clicking on the file in your codespace’s file browser and choosing Download. - Go to CS50’s Gradescope page.
- Click Problem Set 3 : Runoff.
- Drag and drop your
runoff.c
file to the area that says Drag & Drop. Be sure it has that exact filename! If you upload a file with a different name, the autograder likely will fail when trying to run it. Ensuring you have uploaded files with the correct filename is your responsibility! - Click Upload.
You should see a message that says “Problem Set 3: Runoff submitted successfully!”