Gpu the graphics processing unit which forms images your display

Richy Yun

Math 49s

1. • Mac

   • PC

• Less susceptible to viruses

• User interface

• Graphics and processing speed

• Good support

• RAM

• Hard disk vs Solid state

The first obvious question to ask was which machine they have. If they bought the computer, it must mean they preferred it for one reason or another. 15 people responded with Macs as their first choice, and 10 with PC’s as their first choice, whereas no one responded with a Linux or different operating system. Since this was a simple question with only 3 choices, Macs swept every category, and was the Condorcet winner.

The second question I asked was the reasons why they chose the computer they have. Being personally biased, I researched several articles to get an idea for arguments for one operating system over the other, and came up with the list of choices I provided. Seeing as how there were more Mac users, I quickly assumed that the arguments for owning a Mac, such as it being less susceptible to viruses, would definitely come on top. I also suspected certain choices, such as the user interface or trendiness would have much to do with why people chose the computer they did, at the same time thinking that graphics and processing speed and having more software would definitely be huge deciding factors. However, although ‘Ease of use’ expectedly won the plurality and borda counts, ‘User interface’ won in terms of the top two runoff, the instant run off, least worst defeat, and ranked pairs. Looking at the ranked pairs ordering we see that ‘User interface’ won by just one point to ‘Ease of use’ with ‘Versatility’ a close third. They were then followed by the expected choices, such as running more software, graphics and processing speed, and compatibility with other products. Both susceptibility to viruses and price ranked much lower than expected, coming in seventh and ninth respectively. This was definitely the most interesting set of results.

Preferential_Ballots =

Columns 1 through 12

[2] [ 2] [ 1] [ 1] [ 1] [ 2] [ 1] [1] [Inf] [2] [ 1]

[1] [ 1] [ 2] [ 2] [ 2] [ 1] [ 2] [2] [Inf] [1] [Inf]

[Inf] [Inf] [3] [2] [Inf] [Inf] [Inf] [Inf] [Inf] 'Linux or other'

Column 34

[15] [15] [21] 'Mac'

[10] [10] [] 'PC'

'IRV Winner' 'Mac'

'Borda Count Winner' 'Mac'

[ 0] [ 5] [21] 'Mac' [ 26] [ 0]

[ -5] [ 0] [20] 'PC' [ 15] [ -5]

[-21] [-20] [ 0] 'Linux or other' [-41] [-21]

All 3 pairwise matchups respect the above Ranked Pairs ordering.

'Plurality Winner' 'Mac'

'Top Two Runoff Winner' 'Mac'

Mac is the Condorcet winner.

The Ranked Pairs ordering is shown below.

[ 26] [ 0] [25] 'Mac' [ 5] [21]

[ 15] [ -5] [20] 'PC' [20] []

Preferential_Ballots =

Columns 1 through 11

[ 1] [Inf] [ 2] [Inf] [Inf] [ 1] [ 3] [ 1] [Inf] [Inf] [Inf]

[11] [Inf] [11] [Inf] [ 9] [Inf] [Inf] [Inf] [Inf] [Inf] [Inf]

[ 5] [Inf] [ 5] [Inf] [ 6] [Inf] [ 5] [Inf] [Inf] [Inf] [Inf]

[12] [Inf] [12] [Inf] [ 5] [Inf] [Inf] [Inf] [Inf] [Inf] [Inf]

[ 8] [ 5] [Inf] [ 3] [ 2] [ 3] [ 2] [Inf] [ 3] [ 3] [ 1]

[ 9] [ 3] [Inf] [Inf] [ 5] [Inf] [ 8] [Inf] [ 1] [ 5] [ 3]

[ 6] [ 7] [Inf] [ 2] [Inf] [ 7] [ 7] [Inf] [ 6] [ 7] [ 8]

[ 4] [ 2] [Inf] [Inf] [Inf] [Inf] [ 5] [Inf] [11] [ 4] [ 4]

[ 3] [Inf] [ 2] [Inf] [Inf] [Inf] [ 4] [Inf] [Inf] [Inf]

[ 2] [ 1] [ 1] [Inf] [ 1] [Inf] [ 2] [Inf] [Inf] [ 5]

[ 8] [ 4] [ 6] [Inf] [Inf] [Inf] [Inf] [Inf] [Inf] [ 7]

[ 7] [Inf] [ 4] [Inf] [Inf] [Inf] [Inf] [Inf] [Inf] [Inf]

'Runs more and bette' [10]

'Less susceptible to' [ 7]

'Ease of use' [ 5]

'Graphics and proces' [11]

Columns 1 through 12

[1] [1] [1] [1] [1] [1] [1] [1] [] [] [] []

[0] [0] [0] [0] [0] [0] [] [] [] [] [] []

[0] [0] [0] [] [] [] [] [] [] [] [] []

[0] [0] [0] [0] [] [] [] [] [] [] [] []

Column 13

'Versatility'

'Everyone else has i'

'Compatibility with'

'Other'

'Borda Count Winner' 'Ease of use'

'Least Worst Defeat Winner' 'User interface'

[ 0] [ -6] [ -2] [-10] [-12] [ 6] [ 0] [-15] [ -3] [ -1] [ -1]

[ 6] [ 0] [ 1] [ -9] [-12] [13] [ 8] [-13] [ 0] [ 4] [ 2]

[ 0] [ -8] [ -6] [-17] [-14] [ 2] [ 0] [-17] [-10] [ -6] [ -6]

[ 15] [ 13] [ 13] [ -1] [ 6] [21] [17] [ 0] [ 11] [ 13] [ 13]

Columns 12 through 15

[11] 'Price' [ -33] [-15]

[ 4] 'Everyone else has i' [-107] [-21]

[ 8] 'Trendiness' [ -74] [-17]

[ 0] 'Other' [-149] [-19]

RP_Sorted_Margin_of_Victory_Matrix =

[ -9] [-13] [-12] [ 0] [ 0] [ 2] [ 1] [ 4] [ 6] [ 8] [13]

[ -5] [-11] [ -1] [ 0] [ 0] [ 8] [ 4] [ 6] [ 3] [10] [15]

[-17] [-17] [-14] [ -8] [-10] [ -6] [ -6] [ -6] [ 0] [ 0] [ 2]

[-18] [-21] [-12] [-13] [-15] [ -7] [ -8] [ -9] [ -6] [-2] [ 0]

[17] 'Versatility' [ 80] [ -6]

[18] 'Runs more and bette' [ 18] [-13]

[11] 'Price' [ -33] [-15]

[ 8] 'Trendiness' [ -74] [-17]

[1x103 char]

There were 32 voters and 12 choices for this question.

'Borda Count Winner' 'Ease of use'

'Least Worst Defeat Winner' 'User interface'

The kth number to the right of each choice is the margin of victory of that choice over the choice listed k spots below it.

(Most of the numbers on the right should be positive - negative numbers imply cycles in the aggregrate preferences of the voters.)

[ 80] [ -6] [29] 'Versatility' [12] [ 1] [ 9] [ 6] [ 9] [12]

[ 18] [-13] [17] 'Runs more and bette' [ 0] [ 2] [ 1] [ 4] [ 6] [ 8]

[ -33] [-15] [ 6] 'Price' [ 0] [ 6] [11] [] [] []

[ -74] [-17] [ 6] 'Trendiness' [ 2] [ 8] [] [] [] []

[15] [17] [21] [19]

[14] [12] [17] []

[] [] [] []

[] [] [] []

'Which of the following terms are you most familiar with?'

-------------------------------------------

[4] [Inf] [6] [Inf] [ 4] [Inf] [ 3] [ 1] [ 3] [5] [5] [Inf]

[2] [Inf] [4] [Inf] [ 1] [Inf] [ 5] [Inf] [Inf] [4] [4] [Inf]

[3] [Inf] [ 2] [ 1] [ 3] [3] [ 1] [ 1] [Inf] [4] [ 1] [3]

[5] [Inf] [Inf] [ 2] [Inf] [4] [Inf] [Inf] [Inf] [5] [ 2] [5]

[1] [Inf] [Inf] [Inf] [ 1] [Inf] [ 1] [ 1] 'OS'

[2] [Inf] [Inf] [Inf] [ 3] [Inf] [ 2] [ 3] 'RAM'

Column 34

[3]

[6]

Instant_Runoff_Voting_results =

[ 1] [ 1] [] [] [] [] 'CPU'

[ 0] [] [] [] [] [] 'GPU'

'Borda Count Winner' 'OS'

'Least Worst Defeat Winner' 'OS'

[-10] [ 0] [14] [ 13] [ -1] [20] 'RAM' [ 36] [-10]

[-15] [-14] [ 0] [ -4] [-11] [ 7] 'Hard disk vs Solid' [-37] [-15]

[ 0] [ 12] [ 10] [ 13] [15] [20] 'OS' [ 70] [ 0]

[-12] [ 0] [ 1] [ 10] [11] [17] 'CPU' [ 27] [-12]

All 15 pairwise matchups respect the above Ranked Pairs ordering.

-------------- QUESTION 3 SUMMARY -----------------

'Top Two Runoff Winner' 'OS'

'IRV Winner' 'OS'

The Ranked Pairs ordering is shown below.

The Borda Count (1st column), Least Worst Defeat (2nd column), and Ranked Pairs Score (3rd column) are shown to the left of each choice.

[ 27] [-12] [25] 'CPU' [ 1] [10] [11] [17] []

[ 36] [-10] [24] 'RAM' [13] [14] [20] [] []