Planet C has a majority and wins the election. Reddit, Inc. 2023. - ) So, A scores. Spock is the winning candidate, approved by four voters! We must eliminate pink which had the fewest votes with 6. Why or why not? Step 1: Calculate 50 percent of 105,405,100 by multiplying the decimal form of 50 percent, which is 0.50, by 158,394,605: 0.50(105,405,100)=52,702,5500.50(105,405,100)=52,702,550. Borda Count Method - Decision-making tool - SanzuBusinessTraining.com In the event of a tie, the bylaws require the candidate(s) with the fewest votes to be removed from the ballot and a runoff election to be held with the remaining candidates. 8 753 views 1 year ago Voting Methods I have a free calculator to help you find the results of Borda count elections! The preferences of each family member are listed by first initial in the table below. \hline 1^{\text {st }} \text { choice } & \text { Seattle } & \text { Tacoma } & \text { Puyallup } & \text { Olympia } \\ A spoiler is a less popular candidate who takes votes from a more popular candidate with similar positions, swinging the race to another candidate with vastly different views that they would not support. How many students in the class indicated that blue was their favorite color while green was their least favorite color? are licensed under a, Truth Tables for the Conditional and Biconditional, Multiplication and Division in Base Systems, Linear Equations in One Variable with Applications, Linear Inequalities in One Variable with Applications, Graphing Linear Equations and Inequalities, Quadratic Equations with Two Variables with Applications, Systems of Linear Equations in Two Variables, Systems of Linear Inequalities in Two Variables, Probability with Permutations and Combinations, Conditional Probability and the Multiplication Rule, Scatter Plots, Correlation, and Regression Lines, Standard Divisors, Standard Quotas, and the Apportionment Problem, President Barack Obama votes in the 2012 election. 8 How many voters indicated that Option C was their first choice? This is the least whole number greater than 50 percent of the total votes. Lets take a look at the outcomes of U.S. presidential elections to understand more. How many voters indicated that Option A was their first choice? 18 3 & 44 \mathrm{pt} & 14 \mathrm{pt} & \mathrm{B} 20 \mathrm{pt} & 70 \mathrm{pt} & 22 \mathrm{pt} & 80 \mathrm{pt} & \mathrm{G} 39 \mathrm{pt} \\ Lets consider a general case where there are nn candidates. The table below provides an example of a ranked ballot for the 2020 Academy Award nominees for Best Director. A majority is a number equaling more than half, or greater than 50 percent of the total. What is the borda count method? Theory and example - Toolshero As you decide on the voting methods that will be used in your new democracy, budget must be a consideration. An approval voting ballot lists the candidates and provides the option to approve or not approve each candidate. 2 Each row of the preference summary corresponds to a single candidate. There are many types of runoff voting systems, which are voting systems that utilize a runoff election when the first round does not result in a winner. \end{array}\). The answer to the third question is not as clear. Our mission is to improve educational access and learning for everyone. ) \(\begin{array}{|l|l|l|l|l|l|l|l|} McCarthy (M) would be the winner using Borda Count. Step 2: Award each candidate 1 point for a win, half a point for a tie, and 0 points for a loss. The pairwise matchup points for each candidate were: A 1, B. What are the advantages and disadvantages of making types as a first class value? Determine whether there is a winner of the pairwise comparison election represented by the matrix. Explore the Borda count method, learn the formula and how to apply it, and view examples of how this method can be. All of the examples I have found so far is the Borda count for text (e.g input = ['A>B>C>D=E']), which is different from my input. In Example 11.4 and Your Turn 11.4, you were given a list that ordered each voters preferences. How many votes are required for a majority? Developers use AI tools, they just dont trust them (Ep. This makes Planet C a compromise candidate. The juniors at a high school in Central Florida are voting for a theme park to visit for an end of the year field trip. The remaining votes that must be counted for Round 2 are given in the table below. 8 We'd never do this in a real voting situation. It works as I want but not very nice looking code. Voting Theory: Borda count - YouTube The Electoral College was created as a compromise between those authors of the U.S. Constitution who believed Congress should elect the president, and those who believed the citizens should vote directly. How many votes are needed to win by the Hare method? Making statements based on opinion; back them up with references or personal experience. I have a list of ballots that look like A>B>C>D>E and some of them that look like A>B>C=D=E. For example, much like the game of Rock, Paper, Scissors, it is possible for a cyclic pattern to emerge in which each candidate beats the next until the last candidate who beats the first. A third type of ranked voting is the pairwise comparison method, in which the candidates receive a point for each candidate they would beat in a one-on-one election and half a point for each candidate they would tie. 1st B2ndD3rdC4thA Points Bgets 4 points =) Dgets 3 points Cgets 2 points gets 1 point x1.3) The Idea: Award pointsto candidates based on preferenceschedule, then declare the winner to be the candidate with themost points. The method of ranked-choice voting (RCV), also called instant runoff voting (IRV), is a version of the Hare Method, using preference ranking so that, if no single candidate receives a majority, the least popular selections can be eliminated and the results can be recounted, without the need for more elections. \hline 1^{\text {st }} \text { choice } & \mathrm{G} & \mathrm{G} & \mathrm{G} & \mathrm{M} & \mathrm{M} & \mathrm{B} & \mathrm{B} \\ Which two candidates tied in the second round? These choices are reflected in the following table. I have a large preference schedule and I'd prefer not to do all this math by hand so I figured I could do it in excel. How do you decide when the result is a tie? Once all the points are figured out, they must be added together, and the candidate with the most points wins. + To subscribe to this RSS feed, copy and paste this URL into your RSS reader. If there is not a winner, explain why. \hline 3^{\text {rd }} \text { choice } & \text { Olympia } & \text { Olympia } & \text { Olympia } & \text { Puyallup } \\ Consider the results of the 2018 U.S. Senate primary for Maryland. The ballots are in a text file and each ballot is on its own line. This time, for the sake of simplicity, the group decides to use approval voting to determine the best move in the game. Is it okay to have misleading struct and function names for the sake of encapsulation? 6 Why or why not? Compare the winner and the second-place candidate using the Borda count method to those using the ranked-choice method. The last type of voting system you will consider for your budding democracy is an approval voting system. How many students voted for yellow as their favorite color? On the count of three, each person shows a hand signal for rock, paper, or scissors. Step 1: Determine the number of votes needed to achieve a majority. are not subject to the Creative Commons license and may not be reproduced without the prior and express written We must eliminate red, green, and yellow which had the fewest votes with 0 each. As a Condorcet candidate, Candidate C won all the pairwise matchups against Candidates A, B, D, and E, earning four points. citation tool such as. What is the math? Therefore, it is not possible for Candidate C to tie or lose. 3 Each family member will approve their top two choices. (Python), Count number of times a candidate has been voted for, Python counting votes in election and combining score with names [List], How to Count Votes from List and Store in a Dictionary to Track Number of Votes. The Borda count | Single-Winner Voting Methods ), and the number of votes has to applied by the appropriate point value for each place and thus the points are given to the candidate. Should I sell stocks that are performing well or poorly first? Not the answer you're looking for? The general idea should be rather obvious (read line, parse, assign points, sum it up) so get started and ask when you have problems. Who is the Best Director according to the pairwise comparison method? The winner, Option A, is a Condorcet candidate because Option A won each pairwise comparison. Calculate the points received by each candidate in the pairwise comparison matrix. Calculate the number of votes required to have a majority of the popular vote in the 2016 U.S. Republican Presidential Primary. \hline & 51 & 25 & 10 & 14 \\ Asking for help, clarification, or responding to other answers. The voting results for Florida are given in Table 11.3. Borda Count is another voting method, named for Jean-Charles de Borda, who developed the system in 1770. How many voters indicated that Option B was their first choice? The remaining votes that must be counted for Round 2 are shown in the table below. These occur in the last two columns. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo The Hare Method is another runoff voting system in which only the candidate(s) with the very least votes are eliminated. The Borda count assigns points for each rank on the ballot. Use the results in the following table to answer the questions. Instead, we will need to use some reasoning. First, if no candidate meets the criteria to win an election, you will need a backup plan such as a runoff election. This is the least whole number greater than 50 percent of the total votes. Since the Condorcet candidate wins all matchups, the Condorcet candidate wins n-1n-1 points. This process is repeated until a single candidate receives a plurality and wins the election. How many voters indicated that Option B was their last choice? It follows that the most points a single candidate can win is four points, which would occur if the candidate won every matchup. Depending on a persons perspective, this may be perceived as a flaw in either ranked-choice and plurality systems, or the Borda count method. The summary of approval ballots for Rock, Paper, Scissors, Lizard, Spock is given in the table below. Count the number of first place votes for each candidate. The vote for the Academy Awards uses a ranked ballot. Which candidate is the winner by the Borda count method? Do any candidates appear to be divisive candidates? In any pairwise election with five candidates, each candidate must compete against four other candidates. Are you able to explain how, given the input values you wind up with the output values? Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. The __________________ method is a runoff voting system in which only the candidate(s) with the very least votes are eliminated. By clicking Post Your Answer, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct. The results of two voting rounds are given in the table below. This is the total number of points received by this candidate: 8+18+8+35=698+18+8+35=69. 18 = Apply ranked-choice voting to determine a winner. Asking for help, clarification, or responding to other answers. You have your answer to the third key question! Column 2: 6(6-3)=63=186(6-3)=63=18, Column 4: 7(6-1)=75=357(6-1)=75=35, Step 2: Find the sum of the points received in each column. Legal. Refer to Table 11.6 for the following exercises. A pairwise comparison matrix is given. Ballot 1st B2ndD3rdC4thA Points Bgets 4 points =) Dgets 3 points Cgets 2 points gets 1 point If there is a winner, determine whether the winner is a Condorcet candidate. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. I want all the ballots in the text file to be counted and the votes be added up. 4 This process can also be combined into one step as shown here. The ________________ method is a system of voting using ranked ballots (or multiple elections) in which each candidate receives a point for each candidate they would beat in a one-on-one election and half a point for each candidate they would tie. Then the summary of ranked ballots looks like: If you are redistributing all or part of this book in a print format, Draw the initial positions of Mlkky pins in ASCII art. It also allows an individual voter to support more than one candidate equally. For example, if input = [1,2,3,4,5], output will be [0,1,2,3,4]. The rest of the candidates lost to Candidate C. The most points a particular candidate could win if they won matchups with each of the other three candidates is three points. What is the use of the PNP transistor in this circuit? Borda count in Python for list of numbers - Stack Overflow \hline 4^{\text {th }} \text { choice } & \text { Puyallup } & \text { Seattle } & \text { Seattle } & \text { Seattle } \\ They are trying to decide on a restaurant. Therefore, he had a plurality of the popular votes. \end{array}\). - Borda Count Method - YouTube Borda Count In this method, points are assigned to candidates based on their ranking; 1 point for last choice, 2 points for second-to-last choice, and so on. If so, which candidates would advance to the second round? It is a common occurrence for no single candidate to receive a majority of the votes in an election with more than two candidates. 6 The _______________ method is a system of voting using ranked ballots in which each candidate is awarded points corresponding to the number of candidates ranked lower on each ballot. If there is a winner, tell whether the winner is a Condorcet candidate. 4 \text { points } & 4 \cdot 51=204 & 4 \cdot 25= 100 & 4 \cdot 10=40 & 4 \cdot 14=56 \\ For anyone who comes across this, you just need to change this line: for pref,score in borda(ballot).iteritems(): to this: for pref,score in borda(ballot).items(): Do large language models know what they are talking about? Determine Winner of Election by Using the Pairwise Comparison Method. + The pairwise comparison method does not always result in a winner. rev2023.7.5.43524. So far, we have not come across a contradictory example where the Condorcet candidate didn't win, but we cannot know with certainty that it is not possible by looking at examples. What observations can you make about the results? - Go to www.mshearnmath.com/calculators then click on the Borda Count. Extrapolate the results of an approval method election using Table 11.3, the assumptions from Example 11.14, and the additional assumptions that the supporters of Al Gore would all approve Ralph Nader and that half of the supporters of George Bush would approve Pat Buchanan while half would approve Harry Brown. Blue has a majority and wins the election! I have been trying to build the Borda count in Python for a few days. Would there be a second round? This scenario is cited by both opponents and proponents of the Borda count method. A compromise candidate is not the first choice of most of the voters, but is more acceptable to the population as a whole than the other candidates. The votes for where to hold the conference were: \(\begin{array}{|l|l|l|l|l|} It also has appeal for those who want an underdog to have a chance of success because voters will not worry about wasting their vote on a candidate who is not believed likely to win. How many votes does each candidate receive in Round 1? Cookie Notice Which candidate is the winner by the ranked-choice method? 6 The Borda count method, for example, favors compromise candidates over divisive candidates. Perform the subtraction inside each pair of parentheses first, then perform each multiplication, and then perform each addition. Step 2: Count the number of votes for each candidate in the current round of voting. Borda Count Vote Calculator - MSHEARNMATH.COM Creative Commons Attribution License So, A scores 225 points again. Determine which candidate won the primary for the Republicans (R). List the results of each round of voting based on this information and determine which restaurant was ultimately chosen. 6 Then repeat Step 2. The group keeps having a tie because Person A always picks rock, Person B always picks paper which beats rock, and Person C always picks scissors which beats paper, and is beaten by rock! Lets review the ballots from the kindergarten class again, as shown in the table below. Compare your results from question 32 to those from question 26. Display the pairings in a table and indicate the winner of each matchup. Analyze the pairwise comparison matrix. Another aspect of approval voting systems that is a concern to many voters is that candidates in approval elections might encourage their loyal supporters to approve them and only them to avoid giving support to any other candidate. Would there be a second round? An entry of 1 represents the persons first choice; 2, their second; and so on. Fifty percent of 21 is 0.50(21)=10.50.50(21)=10.5. There are four candidates on the ballots. Now, you need to decide which one is best for Imaginaria. Each candidate is assigned a number of points from each ballot equal to the number of candidates to whom he or she is preferred, so that with n candidates, each one receives n - 1 points for a first preference, n - 2 for a second, and so on. Actually, I tried to post my code but it didn't let me. Justify your answer. \(\begin{array}{|l|l|l|l|l|l|l|l|} 4 Determine the winner of an election using the pairwise comparison method. - Use the ranked-choice voting method to determine the winner of the election. Otherwise, eliminate a predetermined number of candidates based on the rules of the election. Blue was ranked higher than 6-1=56-1=5 other colors. Construct a pairwise comparison matrix for the sample summary of ranked ballots in the table above. 5 Step 3: Reallocate the votes to the remaining candidates. + Use Table 11.3 and the following assumptions to extrapolate the results of an approval method election: Step 1: Create a summary of approval ballots based on the given assumptions. In a particular year, five residents were nominated. If that is the case, is it possible that no single candidate will receive more than half of the votes cast? Since each of the other candidates lost to the Condorcet candidate, the most a single candidate could win is n-2n-2. - To learn more, see our tips on writing great answers. Make sure that each time you count the number of first place votes they sum to the number of ballots. e.g. 100 percent of Pat Buchanan supporters would approve George W. Bush. \hline 2^{\text {nd }} \text { choice } & \text { Tacoma } & \text { Puyallup } & \text { Tacoma } & \text { Tacoma } \\ How many votes are required to get a majority? Should I hire an electrician or handyman to move some lights? 586), Starting the Prompt Design Site: A New Home in our Stack Exchange Neighborhood, Testing native, sponsored banner ads on Stack Overflow (starting July 6), Temporary policy: Generative AI (e.g., ChatGPT) is banned, Modify objective function for equal solution distribution. Construct a pairwise comparison matrix for the Best Director ballots. According to Variety magazine, there were 8,469 eligible Oscar voters in 2020. No voters ranked Candidate A as second or third. Elevate your spreadsheet skills with us! There are six members on the board of a Parent Teacher Association (PTA) at a local elementary school: the president (P), the vice president (V), the recording secretary (R), the liaison to the administration (L), the treasurer (T), and the chief fundraiser (C). consent of Rice University. Their approximate locations on a map are shown to the right. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Recall that ranked-choice voting is still the Hare Method where the candidate with the very least number of votes is eliminated each round until a majority is attained. The U.S. Electorial College: Winning the Presidency without a Plurality. This can potentially result in several rounds of runoff elections. A ballot in which a voter is required to give an ordering of their preferences is a ranked ballot, and any voting system in which a voter uses a ranked ballot is referred to as ranked voting. Instead, Bush won. and you must attribute OpenStax. In my case, input = [5, 1, 2, 1, 3] the output should be [4, 0.5, 2, 0.5, 3] since the first input value is the maximum (5), it got 4 (the first position in the output). Approval voting worked out nicely the last time. + Accessibility StatementFor more information contact us atinfo@libretexts.org. The options are Disneys four theme parks: Animal Kingdom, Magic Kingdom, EPCOT Center, or Hollywood Studios. Is there a non-combative term for the word "enemy"? Construct an additional column for each candidates points. This method is one of several Condorcet voting methods, which are methods in which candidates are ranked and then compared pairwise to each other, a candidate having to beat all others in order to win. Second, if the winner is not a Condorcet candidate, then there is at least one candidate who beat the winner in a pairwise matchup and the supporters of that candidate might question the validity of the election. In the future, humans have explored distant solar systems and found three habitable planets which could be colonized. Did this candidate have a majority? How to do the Borda Count method in excel? : r/excel - Reddit 7 Are throat strikes much more dangerous than other acts of violence (that are legal in say MMA/UFC)? But not all votes are decided by a simple majority. Compare and contrast voting methods to identify flaws. Borda Count is another voting method, named for Jean-Charles de Borda, who developed the system in 1770. Position 2,5 are equal, which are 1, so they share scores. A group of mathematicians are getting together for a conference. If a candidate has a majority, that candidate wins the election. This first column tells us that four students ranked blue as their first choice, red as their second choice, pink as their third choice, purple as their fourth choice, yellow as their fifth choice, and green as their sixth choice. If we have 5 numbers (n), Borda count will give the highest score, which is equal to 4 (n-1), to the maximum value. It show as my code is in the wrong format. 1 \text { point } & 1 \cdot 51=51 & 1 \cdot 25=25 & 1 \cdot 10=10 & 1 \cdot 14=14 \\ Example 8. Otherwise, eliminate the candidate(s) with the fewest votes and complete Step 3. The options are Rainbow China, Dough Boys Pizza, Taco City, or Caribbean Flavor. Explain how you know. How many voters indicated that Option A was their last choice? Analyze the pairwise comparison matrix. Since Option B has a Borda score of 820 points, Option B is the winner by the Borda count method. How could the Intel 4004 address 640 bytes if it was only 4-bit? Their preference rankings are given in the following table. Had Gore won either state, he would have had enough electoral votes to win the election. For the following exercises, use Table 11.4 and Table 11.5. As we explore examples of ranked voting, we will summarize the voters preference rankings using a table in which the top row shows the number of ballots that ranked the options in the same order. Want to cite, share, or modify this book? Note: The second and third steps may be repeated as many times as necessary for voting procedures that allow multiple runoffs. { "2.1.01:_Introduction" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "2.1.02:_Preference_Schedules" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "2.1.03:_Plurality" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "2.1.04:_Whats_Wrong_with_Plurality" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "2.1.05:_Insincere_Voting" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "2.1.06:_Instant_Runoff_Voting" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "2.1.07:_Whats_Wrong_with_IRV" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "2.1.08:_Borda_Count" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "2.1.09:_Whats_Wrong_with_Borda_Count" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "2.1.10:_Copelands_Method_(Pairwise_Comparisons)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "2.1.11:_Whats_Wrong_with_Copelands_Method" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "2.1.12:_So_Wheres_the_Fair_Method" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "2.1.13:_Approval_Voting" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "2.1.14:_Whats_Wrong_with_Approval_Voting" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "2.1.15:_Voting_in_America" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "2.1.16:_Exercises" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "2.1.17:_Concepts" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "2.1.18:_Exploration" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()" }, { "2.01:_Voting_Theory" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "2.02:_Apportionment" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()" }, [ "article:topic", "license:ccbysa", "transcluded:yes", "authorname:lippman", "Borda Count", "source[1]-math-36232" ], https://math.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fmath.libretexts.org%2FCourses%2FAmerican_River_College%2FMath_300%253A_My_Math_Ideas_Textbook_(Kinoshita)%2F02%253A_Voting_Theory_and_Apportionment%2F2.01%253A_Voting_Theory%2F2.1.08%253A_Borda_Count, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), Seattle: \(204 + 25 + 10 + 14 = 253\) points, Tacoma: \(153 + 100 + 30 + 42 = 325\) points, Puyallup: \(51 + 75 + 40 + 28 = 194\) points, Olympia: \(102 + 50 + 20 + 56 = 228\) points.
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