Solution
Turnout Table
| Amiya ↓ Ramya → | Staid | Vigorous |
|---|---|---|
| Staid | Turnout = 40% A, R = {½, ½} | Turnout = 60% A, R = {⅓, ⅔} |
| Vigorous | Turnout = 60% A, R = {⅔, ⅓} | Turnout = 80% A, R = {½, ½} |
From the first two statements, we can make the following table :-
In this table first column shows type of campaign amiya chose and first row shows type of campaign ramya chose.
according to clue 1, percentage of students voting in the election will be 20 times the sum of the levels of campaigning of the two students
where level 1 = staid campaign
and, level 2 = vigorous campaign
therefore in the table - voter turnout will be - 20* (level of campaign of ramya + level of campaign of amiya)
therefore in the table for example if amiya had chose a staid campaign (level 1)
and Ramya also chose a staid campaign (level 1)
then their voter turnout will be = ( 20 \times (1 + 1) = 40% )
Turnout Table
| Amiya ↓ Ramya → | Staid | Vigorous |
|---|---|---|
| Staid | Turnout = 40% A, R = {½, ½} | Turnout = 60% A, R = {⅓, ⅔} |
| Vigorous | Turnout = 60% A, R = {⅔, ⅓} | Turnout = 80% A, R = {½, ½} |
A and R is the percentage of votes for each candidate which is proportional to the levels of their campaigns.
i.e., if amiya chose vigorous campaign (level 2) while ramya chose staid campaign (level 1)
Then, percentage of votes for each amiya will be 2/3 and for ramya will be 1/3.
Strategy Table
| Amiya ↓ Ramya → | Attack | Issues |
|---|---|---|
| Attack | 10% - A → No Vote 10% - R → No Vote | 10% - A → R 10% - A → No Vote |
| Issues | 20% - R → A 5% - R → No Vote | No change |
This is the table we can form ,from the further information given in the question directly.
Forming a table like this will help us to rationalize and comprehend the data more easily.
Turnout Table
| Amiya ↓ Ramya → | Staid | Vigorous |
|---|---|---|
| Staid | Turnout = 40% A, R = {½, ½} | Turnout = 60% A, R = {⅓, ⅔} |
| Vigorous | Turnout = 60% A, R = {⅔, ⅓} | Turnout = 80% A, R = {½, ½} |
Strategy Table
| Amiya ↓ Ramya → | Attack | Issues |
|---|---|---|
| Attack | 10% - A → No Vote 10% - R → No Vote | 10% - A → R 10% - A → No Vote |
| Issues | 20% - R → A 5% - R → No Vote | No change |
Since we want maximum number of votes for Amiya, consider both of them runs a vigorous campaign.
Total votes turnout = 20 * (2 + 2)% = 80%.
Both of them receive 40% of the votes. We know Amiya’s campaign is focusing on issues. Since we want maximum votes for Amiya, Ramya runs a campaign attacking Amiya. Therefore, 20% of the students who would have otherwise voted for Ramya will vote for Amiya, another 5% who would have otherwise voted for Ramya will not vote at all.
Amiya will receive 40 + 20% of 40 = 48% and Ramya would lose 8% (20% of 40) and another 2% (5% of 40). Ramya will receive 40 - 8 - 2 = 30%.
Maximum percentage of votes Amiya receives is 48%.