Correct

宁可 vs 宁肯 vs 宁愿

/ nìngkě vs nìngkěn vs nìngyuàn /
Strokes

Definition

宁可, 宁肯 and 宁愿 are all Connections, which means “would rather; more willingly sometimes the choice may not be very satisfactory either”.

Example

宁可, 宁肯 and 宁愿, may be used in the first clause in concert with 也不 in the second clause or used in the second clause in concert with 与其 in the first clause.
In example ①, the two clauses can be reversed.
1
nìng
宁可
  
(
nìngkěn
宁肯
  
)
  
(
nìngyuàn
宁愿
  
)
chē
骑车
  
,
yuàn
zài
shang
路上
sān
xiǎoshí
小时
  
(
chē
  
)
  

He would rather go by bike than be in a traffic jam for three hours.

2
与其
gěi
jiā
大家
zēngjiā
增加
dān
负担
  
,
nìng
宁可
  
(
nìngkěn
宁肯
  
)
  
(
nìngyuàn
宁愿
  
)
  

I would rather do it by myself than make you do more.

3
bu
yuàn
愿意
zài
shang
路上
sān
xiǎoshí
小时
  
(
chē
  
)
  
,
nìng
宁可
  
(
nìngkěn
宁肯
  
)
  
(
nìngyuàn
宁愿
  
)
chē
骑车
  

He would rather go by bike than be in a traffic jam for three hours.

宁可 and 宁肯 used, when the side given up is very obvious or unnecessary to tell clearly, only the choice is told.
Here there is usually (才) 保险,的好, etc. at the end of the sentence. In this case,宁愿 is not usually used.
4
men
我们
nìng
宁可
  
(
nìngkěn
宁肯
  
)
zǎo
diǎnr  
点儿
chū
出发
cái
bǎoxiǎn
保险
  

We'd rather start earlier so as to be punctual.

5
Nìng
宁可
  
(
nìngkěn
宁肯
  
)
shǎo
chī
diǎnr  
一点儿
de
hǎo
  

I would rather eat less.

宁愿 more or less retains the meaning of 宁可愿意 and, therefore, can function as the predicate.
The usages also insinuate a choice after comparison, of 主队 and 客队 in examples ⑥ and of 他 and 其他人 in example ⑦.

If 宁可 or 宁肯 is used, 让 must be added: ……让客队胜利,……让他当领导.
6
nìngyuàn
宁愿
duì
客队
shèng
胜利
  

I would rather the visiting team had won.

7
nìngyuàn
宁愿
dāng
lǐngdǎo
领导
  

I prefer that he is our leader.